## Akiyama, Shigeki

Compute Distance To:
 Author ID: akiyama.shigeki Published as: Akiyama, Shigeki; Akiyama, S. External Links: ORCID
 Documents Indexed: 112 Publications since 1988 3 Contributions as Editor Co-Authors: 54 Co-Authors with 76 Joint Publications 1,320 Co-Co-Authors
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### Co-Authors

 36 single-authored 15 Pethő, Attila 15 Thuswaldner, Jörg Maximilian 11 Brunotte, Horst 6 Tanigawa, Yoshio 5 Lee, Jeong-Yup 4 Kaneko, Hajime 4 Loridant, Benoit 4 Steiner, Wolfgang 3 Borbély, Tibor 3 Caalim, Jonathan V. 3 Frougny, Christiane 3 Sakarovitch, Jacques 3 Scheicher, Klaus 3 Zaïmi, Toufik Mostepha 2 Bassino, Frédérique 2 Berthé, Valérie 2 Gjini, Nertila 2 Imai, Katsunobu 2 Luo, Jun 2 Marsault, Victor 2 Rao, Hui 2 Siegel, Anne 1 Abe, Toshikazu 1 Ahara, Kazushi 1 Barat, Guy 1 Barge, Marcy M. 1 Dorfer, Gerhard 1 Drungilas, Paulius 1 Egami, Shigeki 1 Evertse, Jan-Hendrik 1 Feng, De-Jun 1 Gähler, Franz 1 Harriss, Edmund Orme 1 Hatori, Osamu 1 Hayashi, Hiroko 1 Hiramatsu, Toyokazu 1 Ishikawa, Hideaki 1 Jankauskas, Jonas 1 Jiang, Yunping 1 Kempton, Tom 1 Komatsu, Kazushi 1 Komornik, Vilmos 1 Kwon, DoYong 1 Luca, Florian 1 Matsumoto, Kohji 1 Mercat, Paul 1 Murata, Leo 1 Okazaki, Ryotaro 1 Persson, Tomas 1 Sadahiro, Taizo 1 Shirasaka, Masayuki 1 Sugita, Hiroshi 1 Suzuki, Tomonari 1 Wheeler, John C. 1 Williams, Paul T. 1 Winkler, Reinhard
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### Serials

 8 RIMS Kokyuroku 6 Journal of Number Theory 5 Acta Arithmetica 5 Journal of the Mathematical Society of Japan 3 Advances in Mathematics 3 Nagoya Mathematical Journal 3 Discrete & Computational Geometry 3 Indagationes Mathematicae. New Series 3 Discrete Mathematics and Theoretical Computer Science. DMTCS 3 Uniform Distribution Theory 2 Nonlinearity 2 Periodica Mathematica Hungarica 2 Geometriae Dedicata 2 Hiroshima Mathematical Journal 2 Monatshefte für Mathematik 2 Osaka Journal of Mathematics 2 Proceedings of the Japan Academy. Series A 2 Ergodic Theory and Dynamical Systems 2 Acta Mathematica Hungarica 2 Linear Algebra and its Applications 2 Discrete and Continuous Dynamical Systems 1 Astrophysics and Space Science 1 Computers & Mathematics with Applications 1 Israel Journal of Mathematics 1 Journal of Mathematical Analysis and Applications 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Mathematics of Computation 1 Acta Scientiarum Mathematicarum 1 Archiv der Mathematik 1 Canadian Mathematical Bulletin 1 Functiones et Approximatio. Commentarii Mathematici 1 Japanese Journal of Mathematics. New Series 1 Publicationes Mathematicae 1 Theoretical Computer Science 1 Tsukuba Journal of Mathematics 1 Topology and its Applications 1 European Journal of Combinatorics 1 Kobe Journal of Mathematics 1 Information and Computation 1 Journal of the Ramanujan Mathematical Society 1 Mathematica Pannonica 1 IMRN. International Mathematics Research Notices 1 Journal de Théorie des Nombres de Bordeaux 1 Acta Mathematica et Informatica Universitatis Ostraviensis 1 The Ramanujan Journal 1 Acta Mathematica Academiae Paedagogicae Nyíregyháziensis. New Series 1 Nihonkai Mathematical Journal 1 Central European Journal of Mathematics 1 Advanced Studies in Pure Mathematics 1 Lecture Notes in Mathematics 1 RIMS Kôkyûroku Bessatsu 1 Science China. Mathematics 1 Journal of Fractal Geometry 1 Actes des Rencontres du C.I.R.M.
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### Fields

 90 Number theory (11-XX) 38 Dynamical systems and ergodic theory (37-XX) 24 Convex and discrete geometry (52-XX) 18 Measure and integration (28-XX) 12 Computer science (68-XX) 5 General topology (54-XX) 3 General and overarching topics; collections (00-XX) 3 Combinatorics (05-XX) 3 Field theory and polynomials (12-XX) 2 Algebraic geometry (14-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Special functions (33-XX) 2 Operator theory (47-XX) 1 Mathematical logic and foundations (03-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Geometry (51-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Astronomy and astrophysics (85-XX)

### Citations contained in zbMATH Open

88 Publications have been cited 810 times in 436 Documents Cited by Year
Analytic continuation of multiple zeta-functions and their values at non-positive integers. Zbl 0972.11085
Akiyama, Shigeki; Egami, Shigeki; Tanigawa, Yoshio
2001
Cubic Pisot units with finite beta expansions. Zbl 1001.11038
Akiyama, Shigeki
2000
Generalized radix representations and dynamical systems. I. Zbl 1110.11003
Akiyama, S.; Borbély, T.; Brunotte, H.; Pethő, A.; Thuswaldner, J. M.
2005
On the boundary of self-affine tilings generated by Pisot numbers. Zbl 1032.11033
Akiyama, Shigeki
2002
Powers of rationals modulo 1 and rational base number systems. Zbl 1214.11089
Akiyama, Shigeki; Frougny, Christiane; Sakarovitch, Jacques
2008
Multiple zeta values at non-positive integers. Zbl 1002.11069
Akiyama, Shigeki; Tanigawa, Yoshio
2001
A survey on topological properties of tiles related to number systems. Zbl 1073.37017
Akiyama, Shigeki; Thuswaldner, Jörg M.
2004
Self affine tiling and Pisot numeration system. Zbl 0999.11065
Akiyama, Shigeki
1999
On the Pisot substitution conjecture. Zbl 1376.37043
Akiyama, S.; Barge, M.; Berthé, V.; Lee, J.-Y.; Siegel, A.
2015
Generalized radix representations and dynamical systems. II. Zbl 1142.11055
Akiyama, Shigeki; Brunotte, Horst; Pethő, Attila; Thuswaldner, Jörg M.
2006
The topological structure of fractal tilings generated by quadratic number systems. Zbl 1123.11004
Akiyama, Shigeki; Thuswaldner, J. M.
2005
Pisot numbers and greedy algorithm. Zbl 0919.11063
Akiyama, Shigeki
1998
On analytic continuation of multiple $$L$$-functions and related zeta functions. Zbl 1028.11058
Akiyama, Shigeki; Ishikawa, Hideaki
2002
Boundary parametrization of self-affine tiles. Zbl 1226.28006
Akiyama, Shigeki; Loridant, Benoît
2011
A certain finiteness property of Pisot number systems. Zbl 1052.11055
Akiyama, Shigeki; Rao, Hui; Steiner, Wolfgang
2004
Boundary of central tiles associated with Pisot beta-numeration and purely periodic expansions. Zbl 1190.11005
Akiyama, Shigeki; Barat, Guy; Berthé, Valérie; Siegel, Anne
2008
Symmetric shift radix systems and finite expansions. Zbl 1164.11007
Akiyama, Shigeki; Scheicher, Klaus
2007
New criteria for canonical number systems. Zbl 1049.11008
Akiyama, Shigeki; Rao, Hui
2004
On the connectedness of self-affine attractors. Zbl 1063.37008
Akiyama, Shigeki; Gjini, Nertila
2004
Discrete spectra and Pisot numbers. Zbl 1285.11106
Akiyama, Shigeki; Komornik, Vilmos
2013
On canonical number systems. Zbl 0988.68101
Akiyama, Shigeki; Pethő, Attila
2002
A self similar tiling generated by the minimal Pisot number. Zbl 1024.11066
1998
On the boundary connectedness of connected tiles. Zbl 1070.37010
Luo, Jun; Akiyama, Shigeki; Thuswaldner, Jörg M.
2004
Topological properties of two-dimensional number systems. Zbl 1012.11072
Akiyama, Shigeki; Thuswaldner, Jörg M.
2000
Calculation of values of $$L$$-functions associated to elliptic curves. Zbl 0923.11100
Akiyama, Shigeki; Tanigawa, Yoshio
1999
On the fundamental group of the Sierpiński-gasket. Zbl 1182.57001
Akiyama, S.; Dorfer, G.; Thuswaldner, J. M.; Winkler, R.
2009
Algorithm for determining pure pointedness of self-affine tilings. Zbl 1219.37013
Akiyama, Shigeki; Lee, Jeong-Yup
2011
Connectedness of number theoretic tilings. Zbl 1162.11366
Akiyama, Shigeki; Gjini, Nertila
2005
Isometries of the special orthogonal group. Zbl 1297.47038
Abe, Toshikazu; Akiyama, Shigeki; Hatori, Osamu
2013
From number systems to shift radix systems. Zbl 1217.11008
Akiyama, Shigeki; Scheicher, Klaus
2005
Cubic CNS polynomials, notes on a conjecture of W. J. Gilbert. Zbl 1021.11005
Akiyama, Shigeki; Brunotte, Horst; Pethő, Attila
2003
Periodicity of certain piecewise affine planar maps. Zbl 1209.37018
Akiyama, Shigeki; Brunotte, Horst; Pethő, Attila; Steiner, Wolfgang
2008
Boundary parametrization of planar self-affine tiles with collinear digit set. Zbl 1209.28004
Akiyama, Shigeki; Loridant, Benoît
2010
Height reducing problem on algebraic integers. Zbl 1290.11144
Akiyama, Shigeki; Drungilas, Paulius; Jankauskas, Jonas
2012
Mahler’s $$Z$$-number and $$3/2$$ number systems. Zbl 1212.11073
Akiyama, Shigeki
2008
Remarks on a conjecture on certain integer sequences. Zbl 1121.11014
Akiyama, Shigeki; Brunotte, Horst; Pethő, Attila; Steiner, Wolfgang
2006
On the distribution of polynomials with bounded roots. I: Polynomials with real coefficients. Zbl 1305.33006
Akiyama, Shigeki; Pethő, Attila
2014
On the distribution of polynomials with bounded roots. II: Polynomials with integer coefficients. Zbl 1384.11081
Akiyama, Shigeki; Pethő, Attila
2014
Comments on the height reducing property. Zbl 1356.11074
Akiyama, Shigeki; Zaimi, Toufik
2013
Lehmer numbers and an asymptotic formula for $$\pi$$. Zbl 0708.11016
Akiyama, Shigeki
1990
On a generalization of the radix representation – a survey. Zbl 1135.11007
Akiyama, S.; Borbély, T.; Brunotte, H.; Pethő, A.; Thuswaldner, J. M.
2004
Intersecting two-dimensional fractals with lines. Zbl 1111.11006
Akiyama, Shigeki; Scheicher, Klaus
2005
Generalized radix representations and dynamical systems. IV. Zbl 1190.11041
Akiyama, Shigeki; Brunotte, Horst; Pethő, Attila; Thuswaldner, Jörg M.
2008
Generalized radix representations and dynamical systems. III. Zbl 1217.11007
Akiyama, Shigeki; Brunotte, Horst; Pethő, Attila; Thuswaldner, Jörg M.
2008
Positive finiteness of number systems. Zbl 1211.11011
Akiyama, Shigeki
2006
Pentagonal domain exchange. Zbl 1316.37024
Akiyama, Shigeki; Harriss, Edmund
2013
On the least common multiple of Lucas subsequences. Zbl 1306.11002
Akiyama, Shigeki; Luca, Florian
2013
Overlap coincidence to strong coincidence in substitution tiling dynamics. Zbl 1348.37027
Akiyama, Shigeki; Lee, Jeong-Yup
2014
On the pure Jacobi sums. Zbl 0849.11094
Akiyama, Shigeki
1996
A criterion to estimate the least common multiple of sequences and asymptotic formulas for $$\zeta(3)$$ arising from recurrence relation of an elliptic function. Zbl 0860.11044
Akiyama, Shigeki
1996
Salem numbers and uniform distribution modulo 1. Zbl 1072.11053
Akiyama, Shigeki; Tanigawa, Yoshio
2004
Constructions of Pisot and Salem numbers with flat palindromes. Zbl 1178.11069
Akiyama, Shigeki; Kwon, Do Yong
2008
Characterisation of the numbers which satisfy the height reducing property. Zbl 1308.11096
Akiyama, Shigeki; Thuswaldner, Jörg M.; Zaïmi, Toufik
2015
Comments on the height reducing property. II. Zbl 1308.11097
Akiyama, Shigeki; Thuswaldner, Jörg M.; Zaïmi, Toufik
2015
Symbolic dynamical system and number theoretical tilings. Zbl 1160.37315
Akiyama, Shigeki
2008
A new type of inclusion exclusion principle for sequences and asymptotic formulas for $$\zeta(k)$$. Zbl 0789.11010
Akiyama, Shigeki
1993
On some dimension formula for automorphic forms of weight one. III. Zbl 0655.10027
Hiramatsu, Toyokazu; Akiyama, Shigeki
1988
The dynamical norm conjecture and Pisot tilings. Zbl 0951.11551
Akiyama, Shigeki
1999
Discretized rotation has infinitely many periodic orbits. Zbl 1351.37281
Akiyama, Shigeki; Pethő, Attila
2013
Similar dissection of sets. Zbl 1226.52006
Akiyama, Shigeki; Luo, Jun; Okazaki, Ryotaro; Steiner, Wolfgang; Thuswaldner, Jörg
2011
A note on aperiodic Ammann tiles. Zbl 1252.52018
Akiyama, Shigeki
2012
Arithmetic Meyer sets and finite automata. Zbl 1106.11028
Akiyama, Shigeki; Bassino, Frédérique; Frougny, Christiane
2005
Selberg trace formula for odd weight. I, II. Zbl 0672.10021
Akiyama, Shigeki
1988
Strong coincidence and overlap coincidence. Zbl 1351.52025
Akiyama, Shigeki
2016
Determining pure discrete spectrum for some self-affine tilings. Zbl 1400.37019
Akiyama, Shigeki; Gähler, Franz; Lee, Jeong-Yup
2014
Rotational beta expansion: ergodicity and soficness. Zbl 1379.37010
Akiyama, Shigeki; Caalim, Jonathan
2017
On the $$2^n$$ divisibility of the Fourier coefficients of $$J_q$$ functions and the Atkin conjecture for $$p=2$$. Zbl 0978.11019
Akiyama, Shigeki
1993
The corona limit of Penrose tilings is a regular decagon. Zbl 1350.68194
Akiyama, Shigeki; Imai, Katsunobu
2016
Selberg trace formula for odd weight. II. Zbl 0709.11504
Akiyama, Shigeki
1988
Recent progress related to the classification of canonical number systems. Zbl 1127.11309
Akiyama, Shigeki
2002
Browder’s convergence for one-parameter nonexpansive semigroups. Zbl 1259.47071
Akiyama, Shigeki; Suzuki, Tomonari
2012
Automata for arithmetic Meyer sets. Zbl 1196.68116
Akiyama, Shigeki; Bassino, Frédérique; Frougny, Christiane
2004
Refinements of class number formulas for quadratic fields. Zbl 0973.11519
Akiyama, Shigeki
1994
Primitive matrices over polynomial semirings. Zbl 1242.15030
Akiyama, Shigeki; Brunotte, Horst
2012
Almost uniform distribution modulo 1 and the distribution of primes. Zbl 0902.11027
Akiyama, S.
1998
Calculation of elliptic $$L$$ functions in the critical strip. Zbl 1043.11531
Akiyama, Shigeki; Tanigawa, Yoshio
1996
The Selberg trace formula for modular correspondences. Zbl 0702.11035
Akiyama, Shigeki; Tanigawa, Yoshio
1990
Reducible cubic CNS polynomials. Zbl 1164.11006
Akiyama, Shigeki; Brunotte, Horst; Pethö, Attila
2007
The computation of overlap coincidence in Taylor-Socolar substitution tiling. Zbl 1455.52021
Akiyama, Shigeki; Lee, Jeong-Yup
2014
A note on Hecke’s absolute invariants. Zbl 0754.11013
Akiyama, Shigeki
1992
Finiteness and periodicity of beta expansions – number theoretical and dynamical open problems. Zbl 1474.11022
Akiyama, Shigeki
2009
Substitution and tiling dynamics: introduction to self-inducing structures. Lecture notes from the research school on tiling dynamical systems, CIRM Jean-Morlet Chair, Marseille, France, Fall 2017. Zbl 1454.37001
2020
Generic point equivalence and Pisot numbers. Zbl 1467.37039
Akiyama, Shigeki; Kaneko, Hajime; Kim, Dong Han
2020
Corona limits of tilings: periodic case. Zbl 1416.52013
Akiyama, Shigeki; Caalim, Jonathan; Imai, Katsunobu; Kaneko, Hajime
2019
Invariant measure of rotational beta expansion and Tarski’s Plank problem. Zbl 1365.37003
Akiyama, Shigeki; Caalim, Jonathan
2017
On nearly linear recurrence sequences. Zbl 1414.11020
Akiyama, Shigeki; Evertse, Jan-Hendrik; Pethő, Attila
2017
Boundary parametrization and the topology of tiles. Zbl 1369.28007
Akiyama, Shigeki; Loridant, Benoît
2017
Higher order oscillation and uniform distribution. Zbl 1479.11134
Akiyama, Shigeki; Jiang, Yunping
2019
Substitution and tiling dynamics: introduction to self-inducing structures. Lecture notes from the research school on tiling dynamical systems, CIRM Jean-Morlet Chair, Marseille, France, Fall 2017. Zbl 1454.37001
2020
Generic point equivalence and Pisot numbers. Zbl 1467.37039
Akiyama, Shigeki; Kaneko, Hajime; Kim, Dong Han
2020
Corona limits of tilings: periodic case. Zbl 1416.52013
Akiyama, Shigeki; Caalim, Jonathan; Imai, Katsunobu; Kaneko, Hajime
2019
Higher order oscillation and uniform distribution. Zbl 1479.11134
Akiyama, Shigeki; Jiang, Yunping
2019
Rotational beta expansion: ergodicity and soficness. Zbl 1379.37010
Akiyama, Shigeki; Caalim, Jonathan
2017
Invariant measure of rotational beta expansion and Tarski’s Plank problem. Zbl 1365.37003
Akiyama, Shigeki; Caalim, Jonathan
2017
On nearly linear recurrence sequences. Zbl 1414.11020
Akiyama, Shigeki; Evertse, Jan-Hendrik; Pethő, Attila
2017
Boundary parametrization and the topology of tiles. Zbl 1369.28007
Akiyama, Shigeki; Loridant, Benoît
2017
Strong coincidence and overlap coincidence. Zbl 1351.52025
Akiyama, Shigeki
2016
The corona limit of Penrose tilings is a regular decagon. Zbl 1350.68194
Akiyama, Shigeki; Imai, Katsunobu
2016
On the Pisot substitution conjecture. Zbl 1376.37043
Akiyama, S.; Barge, M.; Berthé, V.; Lee, J.-Y.; Siegel, A.
2015
Characterisation of the numbers which satisfy the height reducing property. Zbl 1308.11096
Akiyama, Shigeki; Thuswaldner, Jörg M.; Zaïmi, Toufik
2015
Comments on the height reducing property. II. Zbl 1308.11097
Akiyama, Shigeki; Thuswaldner, Jörg M.; Zaïmi, Toufik
2015
On the distribution of polynomials with bounded roots. I: Polynomials with real coefficients. Zbl 1305.33006
Akiyama, Shigeki; Pethő, Attila
2014
On the distribution of polynomials with bounded roots. II: Polynomials with integer coefficients. Zbl 1384.11081
Akiyama, Shigeki; Pethő, Attila
2014
Overlap coincidence to strong coincidence in substitution tiling dynamics. Zbl 1348.37027
Akiyama, Shigeki; Lee, Jeong-Yup
2014
Determining pure discrete spectrum for some self-affine tilings. Zbl 1400.37019
Akiyama, Shigeki; Gähler, Franz; Lee, Jeong-Yup
2014
The computation of overlap coincidence in Taylor-Socolar substitution tiling. Zbl 1455.52021
Akiyama, Shigeki; Lee, Jeong-Yup
2014
Discrete spectra and Pisot numbers. Zbl 1285.11106
Akiyama, Shigeki; Komornik, Vilmos
2013
Isometries of the special orthogonal group. Zbl 1297.47038
Abe, Toshikazu; Akiyama, Shigeki; Hatori, Osamu
2013
Comments on the height reducing property. Zbl 1356.11074
Akiyama, Shigeki; Zaimi, Toufik
2013
Pentagonal domain exchange. Zbl 1316.37024
Akiyama, Shigeki; Harriss, Edmund
2013
On the least common multiple of Lucas subsequences. Zbl 1306.11002
Akiyama, Shigeki; Luca, Florian
2013
Discretized rotation has infinitely many periodic orbits. Zbl 1351.37281
Akiyama, Shigeki; Pethő, Attila
2013
Height reducing problem on algebraic integers. Zbl 1290.11144
Akiyama, Shigeki; Drungilas, Paulius; Jankauskas, Jonas
2012
A note on aperiodic Ammann tiles. Zbl 1252.52018
Akiyama, Shigeki
2012
Browder’s convergence for one-parameter nonexpansive semigroups. Zbl 1259.47071
Akiyama, Shigeki; Suzuki, Tomonari
2012
Primitive matrices over polynomial semirings. Zbl 1242.15030
Akiyama, Shigeki; Brunotte, Horst
2012
Boundary parametrization of self-affine tiles. Zbl 1226.28006
Akiyama, Shigeki; Loridant, Benoît
2011
Algorithm for determining pure pointedness of self-affine tilings. Zbl 1219.37013
Akiyama, Shigeki; Lee, Jeong-Yup
2011
Similar dissection of sets. Zbl 1226.52006
Akiyama, Shigeki; Luo, Jun; Okazaki, Ryotaro; Steiner, Wolfgang; Thuswaldner, Jörg
2011
Boundary parametrization of planar self-affine tiles with collinear digit set. Zbl 1209.28004
Akiyama, Shigeki; Loridant, Benoît
2010
On the fundamental group of the Sierpiński-gasket. Zbl 1182.57001
Akiyama, S.; Dorfer, G.; Thuswaldner, J. M.; Winkler, R.
2009
Finiteness and periodicity of beta expansions – number theoretical and dynamical open problems. Zbl 1474.11022
Akiyama, Shigeki
2009
Powers of rationals modulo 1 and rational base number systems. Zbl 1214.11089
Akiyama, Shigeki; Frougny, Christiane; Sakarovitch, Jacques
2008
Boundary of central tiles associated with Pisot beta-numeration and purely periodic expansions. Zbl 1190.11005
Akiyama, Shigeki; Barat, Guy; Berthé, Valérie; Siegel, Anne
2008
Periodicity of certain piecewise affine planar maps. Zbl 1209.37018
Akiyama, Shigeki; Brunotte, Horst; Pethő, Attila; Steiner, Wolfgang
2008
Mahler’s $$Z$$-number and $$3/2$$ number systems. Zbl 1212.11073
Akiyama, Shigeki
2008
Generalized radix representations and dynamical systems. IV. Zbl 1190.11041
Akiyama, Shigeki; Brunotte, Horst; Pethő, Attila; Thuswaldner, Jörg M.
2008
Generalized radix representations and dynamical systems. III. Zbl 1217.11007
Akiyama, Shigeki; Brunotte, Horst; Pethő, Attila; Thuswaldner, Jörg M.
2008
Constructions of Pisot and Salem numbers with flat palindromes. Zbl 1178.11069
Akiyama, Shigeki; Kwon, Do Yong
2008
Symbolic dynamical system and number theoretical tilings. Zbl 1160.37315
Akiyama, Shigeki
2008
Symmetric shift radix systems and finite expansions. Zbl 1164.11007
Akiyama, Shigeki; Scheicher, Klaus
2007
Reducible cubic CNS polynomials. Zbl 1164.11006
Akiyama, Shigeki; Brunotte, Horst; Pethö, Attila
2007
Generalized radix representations and dynamical systems. II. Zbl 1142.11055
Akiyama, Shigeki; Brunotte, Horst; Pethő, Attila; Thuswaldner, Jörg M.
2006
Remarks on a conjecture on certain integer sequences. Zbl 1121.11014
Akiyama, Shigeki; Brunotte, Horst; Pethő, Attila; Steiner, Wolfgang
2006
Positive finiteness of number systems. Zbl 1211.11011
Akiyama, Shigeki
2006
Generalized radix representations and dynamical systems. I. Zbl 1110.11003
Akiyama, S.; Borbély, T.; Brunotte, H.; Pethő, A.; Thuswaldner, J. M.
2005
The topological structure of fractal tilings generated by quadratic number systems. Zbl 1123.11004
Akiyama, Shigeki; Thuswaldner, J. M.
2005
Connectedness of number theoretic tilings. Zbl 1162.11366
Akiyama, Shigeki; Gjini, Nertila
2005
From number systems to shift radix systems. Zbl 1217.11008
Akiyama, Shigeki; Scheicher, Klaus
2005
Intersecting two-dimensional fractals with lines. Zbl 1111.11006
Akiyama, Shigeki; Scheicher, Klaus
2005
Arithmetic Meyer sets and finite automata. Zbl 1106.11028
Akiyama, Shigeki; Bassino, Frédérique; Frougny, Christiane
2005
A survey on topological properties of tiles related to number systems. Zbl 1073.37017
Akiyama, Shigeki; Thuswaldner, Jörg M.
2004
A certain finiteness property of Pisot number systems. Zbl 1052.11055
Akiyama, Shigeki; Rao, Hui; Steiner, Wolfgang
2004
New criteria for canonical number systems. Zbl 1049.11008
Akiyama, Shigeki; Rao, Hui
2004
On the connectedness of self-affine attractors. Zbl 1063.37008
Akiyama, Shigeki; Gjini, Nertila
2004
On the boundary connectedness of connected tiles. Zbl 1070.37010
Luo, Jun; Akiyama, Shigeki; Thuswaldner, Jörg M.
2004
On a generalization of the radix representation – a survey. Zbl 1135.11007
Akiyama, S.; Borbély, T.; Brunotte, H.; Pethő, A.; Thuswaldner, J. M.
2004
Salem numbers and uniform distribution modulo 1. Zbl 1072.11053
Akiyama, Shigeki; Tanigawa, Yoshio
2004
Automata for arithmetic Meyer sets. Zbl 1196.68116
Akiyama, Shigeki; Bassino, Frédérique; Frougny, Christiane
2004
Cubic CNS polynomials, notes on a conjecture of W. J. Gilbert. Zbl 1021.11005
Akiyama, Shigeki; Brunotte, Horst; Pethő, Attila
2003
On the boundary of self-affine tilings generated by Pisot numbers. Zbl 1032.11033
Akiyama, Shigeki
2002
On analytic continuation of multiple $$L$$-functions and related zeta functions. Zbl 1028.11058
Akiyama, Shigeki; Ishikawa, Hideaki
2002
On canonical number systems. Zbl 0988.68101
Akiyama, Shigeki; Pethő, Attila
2002
Recent progress related to the classification of canonical number systems. Zbl 1127.11309
Akiyama, Shigeki
2002
Analytic continuation of multiple zeta-functions and their values at non-positive integers. Zbl 0972.11085
Akiyama, Shigeki; Egami, Shigeki; Tanigawa, Yoshio
2001
Multiple zeta values at non-positive integers. Zbl 1002.11069
Akiyama, Shigeki; Tanigawa, Yoshio
2001
Cubic Pisot units with finite beta expansions. Zbl 1001.11038
Akiyama, Shigeki
2000
Topological properties of two-dimensional number systems. Zbl 1012.11072
Akiyama, Shigeki; Thuswaldner, Jörg M.
2000
Self affine tiling and Pisot numeration system. Zbl 0999.11065
Akiyama, Shigeki
1999
Calculation of values of $$L$$-functions associated to elliptic curves. Zbl 0923.11100
Akiyama, Shigeki; Tanigawa, Yoshio
1999
The dynamical norm conjecture and Pisot tilings. Zbl 0951.11551
Akiyama, Shigeki
1999
Pisot numbers and greedy algorithm. Zbl 0919.11063
Akiyama, Shigeki
1998
A self similar tiling generated by the minimal Pisot number. Zbl 1024.11066
1998
Almost uniform distribution modulo 1 and the distribution of primes. Zbl 0902.11027
Akiyama, S.
1998
On the pure Jacobi sums. Zbl 0849.11094
Akiyama, Shigeki
1996
A criterion to estimate the least common multiple of sequences and asymptotic formulas for $$\zeta(3)$$ arising from recurrence relation of an elliptic function. Zbl 0860.11044
Akiyama, Shigeki
1996
Calculation of elliptic $$L$$ functions in the critical strip. Zbl 1043.11531
Akiyama, Shigeki; Tanigawa, Yoshio
1996
Refinements of class number formulas for quadratic fields. Zbl 0973.11519
Akiyama, Shigeki
1994
A new type of inclusion exclusion principle for sequences and asymptotic formulas for $$\zeta(k)$$. Zbl 0789.11010
Akiyama, Shigeki
1993
On the $$2^n$$ divisibility of the Fourier coefficients of $$J_q$$ functions and the Atkin conjecture for $$p=2$$. Zbl 0978.11019
Akiyama, Shigeki
1993
A note on Hecke’s absolute invariants. Zbl 0754.11013
Akiyama, Shigeki
1992
Lehmer numbers and an asymptotic formula for $$\pi$$. Zbl 0708.11016
Akiyama, Shigeki
1990
The Selberg trace formula for modular correspondences. Zbl 0702.11035
Akiyama, Shigeki; Tanigawa, Yoshio
1990
On some dimension formula for automorphic forms of weight one. III. Zbl 0655.10027
Hiramatsu, Toyokazu; Akiyama, Shigeki
1988
Selberg trace formula for odd weight. I, II. Zbl 0672.10021
Akiyama, Shigeki
1988
Selberg trace formula for odd weight. II. Zbl 0709.11504
Akiyama, Shigeki
1988
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### Cited by 436 Authors

 37 Akiyama, Shigeki 37 Thuswaldner, Jörg Maximilian 16 Dubickas, Artūras 15 Loridant, Benoit 13 Pethő, Attila 12 Berthé, Valérie 12 Matsumoto, Kohji 10 Pelantová, Edita 10 Surer, Paul 10 Tanigawa, Yoshio 9 Scheicher, Klaus 9 Steiner, Wolfgang 9 Tsumura, Hirofumi 8 Luo, Jun 8 Masáková, Zuzana 8 Onozuka, Tomokazu 8 Vávra, Tomáš 7 Baake, Michael 7 Brunotte, Horst 7 Frougny, Christiane 7 Rao, Hui 7 Sirvent, Víctor F. 6 Jankauskas, Jonas 6 Jiang, Kan 6 Lau, Kasing 6 Lee, Jeong-Yup 6 Leung, King-Shun 6 Luo, Jun Jason 6 Madritsch, Manfred G. 6 Zaïmi, Toufik Mostepha 5 Grimm, Uwe 5 Komori, Yasushi 5 Ngai, Sze-Man 5 Siegel, Anne 4 Baker, Simon 4 Barge, Marcy M. 4 Dajani, Karma 4 Drungilas, Paulius 4 Ito, Shunji 4 Kirschenhofer, Peter 4 Kiuchi, Isao 4 Minervino, Milton 4 Okamoto, Takuya 4 Rigo, Michel 4 Saha, Biswajyoti 4 Sakarovitch, Jacques 4 Vivaldi, Franco 4 Xi, Lifeng 3 Barnsley, Michael Fielding 3 Bernat, Julien 3 Bruin, Henk 3 Conner, Gregory R. 3 Gähler, Franz 3 Hbaib, Mohamed 3 Hejda, Tomáš 3 Kalle, Charlene 3 Kanemitsu, Shigeru 3 Kirat, Ibrahim 3 Kong, Derong 3 Kwon, DoYong 3 Marsault, Victor 3 Masri, Riad 3 Nakamura, Takashi 3 Pankowski, Łukasz 3 Sadahiro, Taizo 3 Salehi, Sadegh 3 Sanna, Carlo 3 Sellami, Tarek 3 Shutov, Anton V. 3 Taghavi Jelodar, Ali 3 van de Woestijne, Christiaan E. 3 Vignat, Christophe 3 Vince, Andrew 3 Viswanadham, G. K. 3 Yang, Yamin 3 Zhao, Jianqiang 3 Ziegler, Volker 2 Alaca, Şaban 2 Allouche, Jean-Paul Simon 2 Banerjee, Debika 2 Barat, Guy 2 Caalim, Jonathan V. 2 Damanik, David 2 Deng, Guotai 2 Deng, Qirong 2 Dombek, Daniel 2 Ei, Hiromi 2 Fischer, Hanspeter 2 Fuchs, Clemens 2 Gaál, Marcell 2 González, Josep R. 2 Guo, Li 2 Hirose, Minoru 2 Inam, Ilker 2 Jiménez-Urroz, Jorge 2 Jiu, Lin 2 Jolivet, Timo 2 Kaneko, Hajime 2 Kempton, Tom 2 Komornik, Vilmos ...and 336 more Authors
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### Cited in 134 Serials

 31 Journal of Number Theory 19 Monatshefte für Mathematik 16 Indagationes Mathematicae. New Series 14 Theoretical Computer Science 14 Acta Mathematica Hungarica 12 International Journal of Number Theory 11 Journal of Mathematical Analysis and Applications 10 Advances in Mathematics 9 Annales de l’Institut Fourier 9 Geometriae Dedicata 9 Proceedings of the American Mathematical Society 9 Transactions of the American Mathematical Society 9 Journal de Théorie des Nombres de Bordeaux 9 The Ramanujan Journal 8 Discrete & Computational Geometry 7 Osaka Journal of Mathematics 7 Topology and its Applications 6 Archiv der Mathematik 6 Mathematische Zeitschrift 6 Ergodic Theory and Dynamical Systems 6 Discrete and Continuous Dynamical Systems 5 Functiones et Approximatio. Commentarii Mathematici 5 Nagoya Mathematical Journal 5 Tokyo Journal of Mathematics 5 Linear Algebra and its Applications 5 Fractals 4 Discrete Mathematics 4 Israel Journal of Mathematics 4 Acta Arithmetica 4 Manuscripta Mathematica 4 Advances in Applied Mathematics 4 Experimental Mathematics 4 Journal of Mathematical Sciences (New York) 4 Finite Fields and their Applications 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Mathematics of Computation 3 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 3 Journal of Algebra 3 Journal of the Mathematical Society of Japan 3 Proceedings of the Japan Academy. Series A 3 Quaestiones Mathematicae 3 Tsukuba Journal of Mathematics 3 Journal of Symbolic Computation 3 Integers 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Bulletin of the Australian Mathematical Society 2 Letters in Mathematical Physics 2 Lithuanian Mathematical Journal 2 Journal of Computational and Applied Mathematics 2 St. Petersburg Mathematical Journal 2 Bulletin des Sciences Mathématiques 2 Journal of Difference Equations and Applications 2 Chaos 2 Journal of Integer Sequences 2 RAIRO. Theoretical Informatics and Applications 2 Central European Journal of Mathematics 2 Chebyshevskiĭ Sbornik 2 Science China. Mathematics 2 RAIRO. Theoretical Informatics and Applications 2 Journal of Fractal Geometry 2 Research in Number Theory 2 Actes des Rencontres du C.I.R.M. 1 Analysis Mathematica 1 Communications in Algebra 1 Computers & Mathematics with Applications 1 Communications in Mathematical Physics 1 Journal of Mathematical Physics 1 Linear and Multilinear Algebra 1 Nonlinearity 1 Nuclear Physics. B 1 Periodica Mathematica Hungarica 1 Rocky Mountain Journal of Mathematics 1 Chaos, Solitons and Fractals 1 Journal of Geometry and Physics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Applied Mathematics and Computation 1 Bulletin of the London Mathematical Society 1 Canadian Mathematical Bulletin 1 Commentationes Mathematicae Universitatis Carolinae 1 Computing 1 Fundamenta Mathematicae 1 Glasgow Mathematical Journal 1 Journal of Computer and System Sciences 1 Journal of the London Mathematical Society. Second Series 1 Kodai Mathematical Journal 1 Mathematische Nachrichten 1 Mathematica Scandinavica 1 Michigan Mathematical Journal 1 Pacific Journal of Mathematics 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Results in Mathematics 1 Tohoku Mathematical Journal. Second Series 1 European Journal of Combinatorics 1 Bulletin of the Korean Mathematical Society 1 Acta Applicandae Mathematicae 1 Annals of Pure and Applied Logic 1 Annals of Global Analysis and Geometry 1 Physica D 1 Information and Computation 1 Forum Mathematicum ...and 34 more Serials
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### Cited in 41 Fields

 310 Number theory (11-XX) 108 Dynamical systems and ergodic theory (37-XX) 96 Measure and integration (28-XX) 72 Convex and discrete geometry (52-XX) 44 Computer science (68-XX) 25 Combinatorics (05-XX) 17 General topology (54-XX) 16 Group theory and generalizations (20-XX) 14 Field theory and polynomials (12-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 11 Manifolds and cell complexes (57-XX) 9 Algebraic topology (55-XX) 8 Functions of a complex variable (30-XX) 8 Special functions (33-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 7 Probability theory and stochastic processes (60-XX) 6 Several complex variables and analytic spaces (32-XX) 5 Mathematical logic and foundations (03-XX) 4 Algebraic geometry (14-XX) 4 Associative rings and algebras (16-XX) 4 Nonassociative rings and algebras (17-XX) 4 Sequences, series, summability (40-XX) 4 Functional analysis (46-XX) 4 Operator theory (47-XX) 4 Geometry (51-XX) 4 Information and communication theory, circuits (94-XX) 3 Commutative algebra (13-XX) 3 Numerical analysis (65-XX) 3 Quantum theory (81-XX) 2 General and overarching topics; collections (00-XX) 2 Potential theory (31-XX) 2 Difference and functional equations (39-XX) 2 Differential geometry (53-XX) 1 History and biography (01-XX) 1 General algebraic systems (08-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Ordinary differential equations (34-XX) 1 Approximations and expansions (41-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Operations research, mathematical programming (90-XX)