Publications (classified by subjects)

Shigeki Akiyama and Pierre Arnoux (Eds), Substitution and Tiling Dynamics: Introduction to Self-inducing Structures, Lecture Note in Mathematics 2273, Springer 2020.

Shigeki Akiyama (Ed), Natural extension of arithmetic algorithms and S-adic system, Lecture Notes from RIMS, B58, Kyoto, 2016. 289 pp.

Shigeki Akiyama, Valérie Berthé, Hui Rao and Takao Komatsu (Eds), Numeration and Substitution 2012, Lecture Notes from RIMS, B46, Kyoto, 2014. xii+247 pp.

Kohji Matsumoto, Shigeki Akiyama, Katusi Fukuyama, Hitoshi Nakada, Hiroshi Sugita and Akio Tamagawa (Eds), Functions in number theory and their probabilistic aspects, Lecture Notes from RIMS, B34, Kyoto, 2012. x+475 pp.

Shigeki Akiyama (Ed), Summer School on the Theory of Uniform Distribution, Lecture Notes from RIMS, B29, Kyoto, 2012. vi+118 pp.

Shigeki Akiyama, Kohji Matsumoto, Leo Murata and Hiroshi Sugita (Eds), Probability and Number Theory — Kanazawa 2005, Advanced Studies in Pure Mathematics, 49. Mathematical Society of Japan, Tokyo, 2007. xviii+558 pp. ISBN: 978-4-931469-43-3.

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Uniform Distribution, Irregularity of Distribution

Shigeki Akiyama, Almost uniform distribution modulo 1 and the distribution of primes, Acta Math. Hungar., vol. 78 (1998) 39 - 44. DVI PS.GZ PS PDF

Shigeki Akiyama and Yoshio Tanigawa, Salem numbers and uniform distribution modulo 1. Publicationes Mathematicae Debrecen vol.64/3-4 (2004) 329-341. PS.GZ PS PDF

Shigeki Akiyama, Christiane Frougny and Jacques Sakarovitch, Powers of rationals modulo 1 and rational base number systems, Israel Journal of Mathematics Vol.168 No.1 (2008) 53-91. PDF

Shigeki Akiyama, Mahler's Z-number and 3/2 number systems, Uniform Distribution Theory , Vol.3 (2008), no. 2, 91--99. PDF

Shigeki Akiyama, Victor Marsault, Jacques Sakarovitch, Auto-similarity in rational base number systems, Combinatorics on words, 34–45, Lecture Notes in Comput. Sci., 8079, Springer, Heidelberg, 2013. PDF

Shigeki Akiyama, Victor Marsault, Jacques Sakarovitch, On subtrees of the representation tree in rational base numeration systems. Discrete Mathematics and Theoretical Computer Science, Vol.20:1 (2018) Paper No. 10, 33 pp. ArXiv

Shigeki Akiyama, De-Jun Feng, Tom Kempton, Tomas Persson, On the Hausdorff Dimension of Bernoulli Convolutions, International Mathematics Research Notices, rny209, Online: 3 September 2018, DOI:10.1093/imrn/rny209 ArXiv

Shigeki Akiyama and Yunping Jiang, Higher Order Oscillation and Uniform Distribution, Uniform Distribution Theory, vol 14 no.1 (2019), 1-10. ArXiv

Shigeki Akiyama, Hajime Kaneko, Dong Han Kim, Generic point equivalence and Pisot numbers, Ergodic Theory and Dynamical Systems , Volume 40 , Issue 12 , December 2020 , pp. 3169 - 3180, DOI: 10.1017/etds.2019.46 ArXiv

Shigeki Akiyama and Hajime Kaneko, Multiplicative analogue of Markoff-Lagrange spectrum and Pisot numbers, Advances in Mathematics, Volume 380, 26 March 2021, 107547, ArXiv

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Number system, Shift Radix system

Shigeki Akiyama, Pisot numbers and greedy algorithm, `Number Theory, Diophantine, Computational and Algebraic Aspects' edited by K.Győry, A.Pethő, V.T.Sós. (1998) 9 - 21, de Gruyter. DVI PS.GZ PS PDF

Shigeki Akiyama, Cubic Pisot Units with finite beta expansions, `Algebraic Number Theory and Diophantine Analysis', ed. by F.Halter-Koch and R.F. Tichy, de Gruyter (2000), 11-26. DVI PS.GZ PS PDF

Shigeki Akiyama and Attila Pethő, On Canonical Number Systems, Theoret. Comp. Sci., vol. 270 (2002) 921-933. DVI PS.GZ PS PDF

Shigeki Akiyama, Horst Brunotte and Attila Pethő, Cubic CNS Polynomials, notes on a conjecture of W.J.Gilbert, J. Math. Anal. and Appl., vol. 281 (2003) 402-415. DVI PS.GZ PS PDF

Shigeki Akiyama and Hui Rao, New criteria for canonical number systems, Acta Arith. vol.111, no.1 (2004), 5-25. DVI PS.GZ PS PDF

Shigeki Akiyama, Tibor Borbély, Horst Brunotte, Attila Pethő, Jörg Thuswaldner, On a generalization of the radix representation---a survey, High primes and misdemeanours: 19-27, Fields Inst. Commun., 41, Amer. Math. Soc., Providence, RI, 2004. PDF

Shigeki Akiyama, Hui Rao and Wolfgang Steiner, A certain finiteness property of Pisot number systems, Journal of Number Theory. vol. 107/1 (2004) 135-160. DVI PS.GZ PS PDF

Shigeki Akiyama, Tibor Borbély, Horst Brunotte, Attila Pethő and Jörg Thuswaldner, Generalized radix representations and dynamical systems I, Acta Math. Hungarica. 108 (2005), no. 3, 207-238. PDF

Shigeki Akiyama and Klaus Scheicher, From number systems to shift radix systems, Nihonkai Math. J. 16 (2005) no. 2, 95-106. PDF

Shigeki Akiyama, Tibor Borbély, Horst Brunotte, Attila Pethő, Jörg Thuswaldner, Basic properties of shift radix systems, Acta Math. Acad. Paedagog. Nyházi. vol. 22 no.1 (2006) 19-25. PDF

Shigeki Akiyama, Horst Brunotte, Attila Pethő, Jörg Thuswaldner, Generalized radix representations and dynamical systems II, Acta Arith. 121 (2006) no. 1 , 21-61. PDF

Shigeki Akiyama, Positive finiteness of number systems, `Number Theory: Tradition and Modernization', ed. by W.Zhang and Y.Tanigawa , DEVM 15, Springer (2006) 1-10. PDF

Shigeki Akiyama and Klaus Scheicher, Symmetric shift radix systems and finite expansions, Mathematica Pannonica, 18 (2007) no. 1, 101--124. PDF

Shigeki Akiyama, Horst Brunotte and Attila Pethő, Reducible cubic CNS polynomials, Periodica Mathematica Hungarica Vol. 55, (2007) no.2, 177-183. PDF

Shigeki Akiyama, Horst Brunotte, Attila Pethő and Jörg Thuswaldner, Generalized radix representations and dynamical systems III, Osaka Journal of Mathematics Vol.45 (2008) no.2, 347-374. PDF

Shigeki Akiyama, Horst Brunotte, Attila Pethő and Jörg Thuswaldner, Generalized radix representations and dynamical systems IV, Indagationes Mathematicae (N.S.), Vol.19 (2008), no. 3, 333--348. PDF

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Fractal Tiling, Tiling Dynamics

Shigeki Akiyama and Taizo Sadahiro, A self-similar tiling generated by the minimal Pisot number, Acta Math. Info. Univ. Ostraviensis, vol.6 (1998) 9-26. PS.GZ PS PDF

Shigeki Akiyama, Self affine tiling and Pisot numeration system, `Number Theory and its Applications', ed. by K. Győry and S. Kanemitsu, Kluwer (1999) 7-17. PS.GZ PS PDF

Shigeki Akiyama and Jörg Thuswaldner, Topological properties of two-dimensional number systems, Journal de Théorie des Nombres de Bordeaux, vol.12 (2000) no.1, 69-79. DVI PS.GZ PS PDF

Shigeki Akiyama, On the boundary of self affine tilings generated by Pisot numbers, Journal of Mathematical Society of Japan, vol. 54 (2002), no. 2, 283-308. PS.GZ PS PDF

Jun Luo, Shigeki Akiyama and Jörg Thuswaldner, On the boundary connectedness of connected tiles, Math. Proc. Cambridge Phil. Soc., vol. 137, no. 2 (2004) 397-410. PS.GZ PS PDF

Shigeki Akiyama and Nertila Gjini, On the connectedness of self-affine attactors, Arch. Math. (Basel) vol.82 (2004) 153-163. PS.GZ PS PDF

Shigeki Akiyama and Jörg Thuswaldner, A survey on topological properties of tiles related to number systems, Geometriae Dedicata. vol. 109 (2004) 89-105. PS.GZ PDF

Shigeki Akiyama and Jörg Thuswaldner, On the Topological Structure of Fractal Tilings Generated by Quadratic Number Systems, Comput. Math. Appl. 49 (2005) 1439-1485. PS.GZ PS PDF

Shigeki Akiyama and Klaus Scheicher, Intersecting two dimensional fractals and lines, Acta Sci. Math. (Szeged) 71 (2005), no.3-4, 555-580. PDF

Shigeki Akiyama and Nertila Gjini, Connectedness of number theoretic tilings, Discret. Math. Theoret. Comput. Sci. 7 (2005) no. 1 , 269-312. PDF

Shigeki Akiyama, Pisot number system and its dual tiling, `Physics and Theoretical Computer Science' , ed. by J.P. Gazeau et al., IOS Press (2007) 133-154. PDF

Shigeki Akiyama, Guy Barat, Valérie Berthé and Anne Siegel, Boundary of central tiles associated with Pisot beta-numeration and purely periodic expansions, Monatshefte für Mathematik Vol.155 (2008) 377-419. PDF

Shigeki Akiyama, Gerhart Dorfer, Reinhart Winkler and Jörg Thuswaldner, On the fundamental group of the Sierpiński-gasket, Topology and its applications, Vol.156 (2009) 1655–1672. PDF

Shigeki Akiyama and Benoît Loridant, Boundary parametrization of planar self-affine tiles with collinear digit set, Science China Math. 53 (2010) No. 9, 2173–2194. PDF

Shigeki Akiyama and Jeong-Yup Lee, Determining quasicrystal structures on substitution tilings, Philosophical Magazine, vol.91 (2011) No.19, 2709–2717. PDF

Shigeki Akiyama and Jeong-Yup Lee, Algorithm for determining pure pointedness of self-affine tilings, Advances in Mathematics 226 (2011) 2855–2883. PDF

Shigeki Akiyama and Benoît Loridant, Boundary parametrization of self-affine tiles, Journal of Mathematical Society of Japan. vol. 63, no.2 (2011) 525-579. ZIPped PS

Shigeki Akiyama and Jeong-Yup Lee, The computation of overlap coincidence in Taylor-Socolar substitution tiling, Osaka Journal of Mathematics, vol. 51 (2014) 597–607. ArXiv

Shigeki Akiyama and Jeong-Yup Lee, Overlap coincidence to strong coincidence in substitution tiling dynamics, European J. Combin. Volume 39, July 2014, Pages 233–243, DOI:10.1016/j.ejc.2014.01.009. PDF

Shigeki Akiyama, Franz Gähler and Jeong-Yup Lee, Determining pure discrete spectrum on some self-affine tilings, Discrete Mathematics and Theoretical Computer Science, vol. 16:3 (2014) 305–316. ArXiv

Shigeki Akiyama, Strong coincidence and overlap coincidence, Discrete and Continuous Dynamical System - A, Pages: 5223 - 5230, Volume 36, Issue 10, October 2016. ArXiv

Shigeki Akiyama and Benoît Loridant, Boundary parametrization and the topology of tiles, Nagoya Math. J., Volume 226 (2016), 127–164, DOI 10.1017/nmj.2016.43 PDF

Shigeki Akiyama and Katsunobu Imai, The corona limit of Penrose tilings is a regular decagon, Lecture Note in Computer Science 9664, M. Cook and T. Neary (Eds.): AUTOMATA 2016, pp. 35–48, 2016, DOI: 10.1007/978-3-319-39300-1. PDF

Kazushi Ahara, Shigeki Akiyama, Hiroko Hayashi and Kazushi Komatsu, Strongly non-periodic hyperbolic tilings using a single vertex configuration, Hiroshima Mathematical Journal, Vol 48, No. 2, July (2018), 133-140. PDF (Open)

Shigeki Akiyama, Jonathan Caalim, Katsunobu Imai and Hajime Kaneko, Corona limits of tilings : Periodic case, Discrete & Computational Geometry, (2019) 61:626–652. DOI: 10.1007/s00454-018-0033-x ArXiv

Jeong-Yup Lee, Shigeki Akiyama, Yasushi Nagai, Cut-and-project schemes for Pisot family substitution tilings, Symmetry 2018, 10(10), 511; PDF (Open)

Dong-il Lee, Shigeki Akiyama, Jeong-Yup Lee, Pure Discrete Spectrum and Regular Model Sets in Unimodular Substitution Tilings on R^d, Acta Crystallographica (2020) A76, 600-610 Open

Shigeki Akiyama, Benoît Loridant, Jörg Thuswaldner, Topology of planar self-affine tiles with collinear digit set, Journal of Fractal Geometry, Volume 8 (2021), 53-93 ArXiv

Yasushi Nagai, Shigeki Akiyama, Jeong-Yup Lee, On arithmetic progressions in non-periodic tilings, Ergodic Theory and Dynamical Systems , Volume 42-9 (2021) 2957-2989 ArXiv

Shigeki Akiyama, Paul Grosskopf, Benoît Loridant, Wolfgang Steiner, Intersecting the twin dragon with rational lines, Journal of Fractal Geometry, to appear ArXiv

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Symbolic Dynamics, Ergodic Theory, Miscellanea

Shigeki Akiyama, Frédérique Bassino and Christiane Frougny, Automata for arithmetic Meyer sets, Proceedings of LATIN 04, Lectures Notes in Computer Science, 2976 (2004) 252-261. PS.GZ PS PDF

Shigeki Akiyama, Frédérique Bassino and Christiane Frougny, Arithmetic Meyer sets and Finite Automata, Inform. and Comput. 201 (2005), no. 2, 199-215. PS PDF

Shigeki Akiyama, Horst Brunotte, Attila Pethő, Wolfgang Steiner, Remarks on a conjecture on certain integer sequences, Periodica Math. Hungarica 52 (2006) no. 1 , 1-17. PDF

Shigeki Akiyama, Horst Brunotte, Attila Pethő and Wolfgang Steiner, Periodicity of certain piecewise affine planar maps, Tsukuba Journal of Mathematics Vol. 32 No.1 (2008) 197-251. PDF

Shigeki Akiyama and Masayuki Shirasaka, Recursively renewable words and coding of irrational rotations, Journal of Mathematical Society of Japan 59 (2007) no.4, 1199-1234. PDF

Shigeki Akiyama and DoYong Kwon, Constructions of Pisot and Salem numbers with flat palindromes, Monatshefte für Mathematik Vol.155 (2008) 265-275. PDF

Shigeki Akiyama, Jun Luo, Ryotaro Okazaki, Wolfgang Steiner and Jörg Thuswaldner, Similar dissection of sets, Geometriae Dedicata, vol.150 (2011) 233–247. PDF

Shigeki Akiyama and Tomonari Suzuki, Browder’s convergence for one-parameter nonexpansive semigroups, Canadian Mathematical Bulletin, vol. 55 (2012), no. 1, 15–25, DOI: 10.4153/CMB-2011-071-9. PDF

Shigeki Akiyama and Horst Brunotte, Primitive matrices over polynomial semirings. Linear Algebra and its Applications, vol.436, Issue 9, 1 May 2012, Pages 3568–3596. PDF

Shigeki Akiyama, A note on aperiodic Ammann tiles, Discrete & Computational Geometry, vol.48 (2012) 702–710, DOI 10.1007/s00454-012-9418-4. PDF

Shigeki Akiyama and Vilmos Komornik, Discrete Spectra and Pisot numbers, Journal of Number Theory, vol. 133 (2013), 375-390, DOI 10.1016/j.jnt.2012.07.015. ArXiv

Shigeki Akiyama and Edmund Harriss, Pentagonal Domain Exchange, Discrete and Continuous Dynamical System -A, Vol. 33, Num.10 (2013) 4375-4400, doi:10.3934/dcds.2013.33.4375. PDF

Shigeki Akiyama and Attila Pethő, Discretized rotation has infinitely many periodic orbits, Nonlinearity vol. 26, no.3 (2013), 871-880, doi:10.1088/0951-7715/26/3/871. ArXiv

Toshikazu Abe, Shigeki Akiyama and Osamu Hatori, Isometries of the special orthogonal group, Linear Algebra and its Applications vol. 439 (2013) 174–188, doi:10.1016/j.laa.2013.03.008. PDF

Shigeki Akiyama, A family of non-sofic beta expansions, Ergodic Theory and Dynamical Systems, Published Online 2014, Volume 36, Issue 2 April 2016, pp. 343-354, DOI:10.1017/etds.2014.60. ArXiv

Shigeki Akiyama, Laszlo Aszalós, Lajos Hajdu, Attila Pethő, Correlation clustering of graphs and integers. Infocommunication Journal, 6 (2014), 3--12. PDF

Shigeki Akiyama and Jonathan Caalim, Rotational beta expansion: Ergodicity and Soficness, Journal of the Mathematical Society of Japan, Volume 69, Number 1 (2017), 397-415. ArXiv

Shigeki Akiyama and Jonathan Caalim, Invariant measure of rotational beta expansion and a problem of Tarski, Discrete & Computational Geometry, March 2017, Volume 57, Issue 2, pp 357–370. ArXiv

Shigeki Akiyama, Spiral Delone sets and three distance theorem, Nonlinearity, Volume 33, Number 5 (2020), 2533--2540 ArXiv

Paul Mercat and Shigeki Akiyama, Yet another characterization of the Pisot substitution conjecture, Chapter 8, in "Substitution and Tiling Dynamics", Lect. Note in Math. 2273, Springer 2020 ArXiv

Shigeki Akiyama, Minimum polyhedron with n vertices, Hiroshima Mathematical J. 51(2): 111-137 (2021), ArXiv

Shigeki Akiyama, Asymptotic formula for balanced words, Journal of Number Theory, Volume 236 (2022) 144-159, ArXiv

Shigeki Akiyama and Hachem Hichri, Periodic expansion of one by Salem numbers, Ergodic Theory and Dynamical Systems, Published Online 14 October 2022 ArXiv

Shigeki Akiyama, Teturo Kamae, Width deviation of convex polygons, To appear in Discrete and Computational Geometry, ArXiv

Shigeki Akiyama, Damien Jamet, Irène Marcovici, Mai-Linh Trân-Công, Self-descriptive Sequences directed by two Periodic Sequences, In Proceedings GASCom 2024, ArXiv

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Automorphic Forms, L-functions, Multiple Zeta

Shigeki Akiyama, On the Fourier coefficients of automorphic forms of triangle groups, Kobe J. Math. 5 (1988), no. 1, 123-131. PDF

Shigeki Akiyama, Selberg trace formula for odd weight I, Proc. Japan Acad. Ser. A Math. Sci. 64 (1988). no. 9, 341-344.

Shigeki Akiyama, Selberg trace formula for odd weight. II, Proc. Japan Acad. Ser. A Math. Sci. 64 (1988). no. 10, 387-388.

Hiramatsu Toyokazu and Shigeki Akiyama, On some dimension formula for automorphic forms of weight one. III, Nagoya Math. J. vol. 111 (1988), 157-163.

Shigeki Akiyama and Yoshio Tanigawa, The Selberg trace formula for modular correspondences, Nagoya Math. J. vol. 117 (1990) 93 - 123.

Shigeki Akiyama, On a certain sum of traces of Hecke operators, Lecture Notes in Math., Springer, vol.1434 (1990), 1 - 10. PDF

Shigeki Akiyama, A note on Hecke's absolute invariants, Journal of the Ramanujan Mathematical Society, vol.7 (1992) no.1, 65 - 81. PDF

Shigeki Akiyama, On the 2ⁿ divisibility of the Fourier coefficients of J_q functions and the Atkin conjecture for p=2, Analytic number theory and related topics, World Scientific Publ., (1993), 1 - 15. DVI PDF (Uncertain remade from an old tex file.)

Shigeki Akiyama and Yoshio Tanigawa, Calculation of values of L-functions associated to elliptic curves, Math. Comp., vol.68, no. 227 (1999) 1201-1231. PDF (A bad copy. Better to visit AMS by the left link.)

Shigeki Akiyama, Shigeki Egami and Yoshio Tanigawa, Analytic continuation of multiple zeta-functions and their values at non-positive integers, Acta Arith., vol.98, no.2 (2001) 107-116. DVI PS.GZ PS PDF

Shigeki Akiyama and Yoshio Tanigawa, Multiple zeta values at non-positive integers, The Ramanujan Journal, vol. 5, no.4 (2001) 327-351. DVI PS.GZ PS PDF

Shigeki Akiyama and Hideaki Ishikawa, On analytic continuation of multiple L-functions and related zeta functions, `Analytic Number Theory', edited by C.Jia and K.Matsumoto, DEVM 6, Kluwer (2002) 1-16. DVI PS.GZ PS PDF

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Analytic Number Theory in general

Shigeki Akiyama, Lehmer numbers and an asymptotic formula for π, Journal of Number Theory, vol.36 (1990) no.3, 328 - 331. PDF

Shigeki Akiyama, A new type of inclusion exclusion principle for sequences and asymptotic formulas for π, Journal of Number Theory, vol.45 (1993) no.2, 200 - 214. PDF

Shigeki Akiyama, A criterion to estimate the least common multiple of sequences and the asymptotic formula for z(3) arising from recurrence relation of an elliptic function, Japanese Journal of Math., vol.22, no.1 (1996), 129 - 146. DVI PS.GZ PS PDF

Shigeki Akiyama, On the pure Jacobi sums, Acta Arith., vol.75, no.2 (1996), 97 - 104. DVI PS.GZ PS PDF

Shigeki Akiyama, Paulius Drungilas and Jonas Jankauskas, Height reducing problem on algebraic integers, Functiones et Approximatio, vol. 47, no. 1 (2012) 105-119, DOI: 10.7169/facm/2012.17.1.9. PDF

Shigeki Akiyama and Toufik Zaïmi, Comments on the height reducing property, Cent. Eur. J. Math., 2013, 11(9), 1616-1627, DOI: 10.2478/s11533-013-0262-4. ArXiv

Shigeki Akiyama and Attila Pethő, On the distribution of polynomials with bounded roots, I. Polynomials with real coefficients, Journal of Mathematical Society of Japan, Vol. 66, No. 3 (2014) 1–23, DOI: 10.2969/jmsj/. PDF

Shigeki Akiyama and Florian Luca, On the least common multiple of Lucas subsequences, Acta Arithmetica, vol. 161, no.4 (2013) 327-349, DOI: 10.4064/aa161-4-2. PDF

Shigeki Akiyama and Attila Pethő, On the distribution of polynomials with bounded roots II. Polynomials with integer coefficients, Uniform Distribution Theory, vol.9 (2014) no. 1, 5-19. PDF

Shigeki Akiyama, Mean divisibility of multinomial coefficients, Journal of Number Theory, vol. 136 (2014) no. 3, 438-459, DOI: 10.1016/j.jnt.2013.10.005. ArXiv

Shigeki Akiyama, Jörg Thuswaldner and Toufik Zaïmi, Characterization of the numbers which satisfy the height reducing property, Indag. Math. vol.26 (2015) 24-27, DOI:10.1016/j.indag.2014.03.003. ArXiv

Shigeki Akiyama, Jörg Thuswaldner and Toufik Zaïmi, Comments on the height reducing property II. Indag. Math. vol. 26 (2015) 28-39. DOI:10.1016/j.indag.2014.07.002. ArXiv

Shigeki Akiyama, Jan-Hendrik Evertse and Attila Pethő, On a Binet-type formula for nearly linear recurrence sequences and its applications, C. Elsholtz, P. Grabner (eds.), Number Theory – Diophantine Problems, Uniform Distribution and Applications, DOI 10.1007/978-3-319-55357-3_1. ArXiv

Shigeki Akiyama and Hajime Kaneko, Curious congruences for cyclotomic polynomials, Research in Number Theory, Volume 8, issue 4, December 2022, ArXiv

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Books
Uniform Distribution, Irregularity of Distribution
Fractal Tiling, Tiling Dynamics
Number system, Shift Radix system
Symbolic Dynamics, Ergodic Theory, Miscellanea
Automorphic Forms, L-functions, Multiple Zeta
Analytic Number Theory in general