Publications (Old → New)

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, Lehmer numbers and an asymptotic formula for π, Journal of Number Theory, vol.36 (1990) no.3, 328 - 331. 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, 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, 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, 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, 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, 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 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 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, 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, 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 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, 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 Attila Pethő, On Canonical Number Systems, Theoret. Comp. Sci., vol. 270 (2002) 921-933. 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

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

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

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 Hui Rao, New criteria for canonical number systems, Acta Arith. vol.111, no.1 (2004), 5-25. 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 and Nertila Gjini, On the connectedness of self-affine attactors, Arch. Math. (Basel) vol.82 (2004) 153-163. 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 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, 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, 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 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, Frédérique Bassino and Christiane Frougny, Arithmetic Meyer sets and Finite Automata, Inform. and Comput. 201 (2005), no. 2, 199-215. 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 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, 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, 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, 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 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, 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 Wolfgang Steiner, Periodicity of certain piecewise affine planar maps, Tsukuba Journal of Mathematics Vol. 32 No.1 (2008) 197-251. 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, 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 and DoYong Kwon, Constructions of Pisot and Salem numbers with flat palindromes, Monatshefte für Mathematik Vol.155 (2008) 265-275. 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

Shigeki Akiyama, Mahler's Z-number and 3/2 number systems, Uniform Distribution Theory , Vol.3 (2008), no. 2, 91--99. 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, Jun Luo, Ryotaro Okazaki, Wolfgang Steiner and Jörg Thuswaldner, Similar dissection of sets, Geometriae Dedicata, vol.150 (2011) 233–247. 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 Tomonari Suzuki, Browder’s convergence for one-parameter nonexpansive semigroups, Canadian Mathematical Bulletin, Online First Apr 6 (2011) doi:10.4153/CMB-2011-071-9. PDF

Shigeki Akiyama, Paulius Drungilas and Jonas Jankauskas, Height reducing problem on algebraic integers, to appear in Functiones et Approximatio, Commentarii Mathematici. 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, To appear in Journal of Number Theory, ArXiv