No.1898

RIMS Kôkyûroku

No.1898

解析的整数論－超越関数の数論的性質とその応用

Analytic Number Theory－Arithmetic Properties of Transcendental Functions and their Applications

RIMS 研究集会報告集

2013/11/05～2013/11/07

田中孝明

Takaaki Tanaka

目　次

1. 変形Riemannゼータ分布とその応用 (解析的整数論 : 超越関数の数論的性質とその応用)---------------------------------------------------1

　　　　東京理科大学理工学部　　　中村隆　(Nakamura,Takashi)

2. Algebraic independence of values of Carlitz multiple polylogarithms (Analytic Number Theory : Arithmetic Properties of Transcendental Functions and their Applications)---6

　　　　九州大学数理学府　　　三柴善範　(Mishiba,Yoshinori)

3. How should we bet on prime number dice? (Analytic Number Theory : Arithmetic Properties of Transcendental Functions and their Applications)---16

　　　　大阪大学大学院理学研究科　　　小川裕之　(Ogawa,Hiroyuki)

4. On a certain trace of Selberg type (Analytic Number Theory : Arithmetic Properties of Transcendental Functions and their Applications)---28

　　　　津山工業高等専門学校　　　吉田英治　(YOSHIDA,Eiji)

5. Independence of complex Cantor series and Cantor products (Analytic Number Theory : Arithmetic Properties of Transcendental Functions and their Applications)---47

　　　　弘前大学理工学研究科 / Department of Mathematics, Faculty of Science, Kasetsart University / Department of Mathematics and Statistics, Faculty of Science, Prince of Songkla University / Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University　　　小松尚夫 / Laohakosol Vichian / Prugsapitak Supawadee / Rattanamoong Jittinart　(Komatsu,Takao / Laohakosol,Vichian / Prugsapitak,Supawadee / Rattanamoong,Jittinart)

6. INTERPOLATING CARLITZ ZETA VALUES (Analytic Number Theory : Arithmetic Properties of Transcendental Functions and their Applications)---58

　　　　Institut Camille Jordan, Faculte des Sciences　　　Pellarin,Federico

7. Mean values of Mordell-Tornheim double zeta-functions (Analytic Number Theory : Arithmetic Properties of Transcendental Functions and their Applications)---70

　　　　立命館大学理工学部 / 名古屋大学多元数理科学研究科　　　岡本卓也 / 小野塚友一　(Okamoto,Takuya / Onozuka,Tomokazu)

8. Algebraic independence of the power series related to the beta expansions of real numbers (Analytic Number Theory : Arithmetic Properties of Transcendental Functions and their Applications)---80

　　　　日本学術振興会・日本大学理工学部　　　金子元　(Kaneko,Hajime)

9. COMPUTING $S$-INTEGRAL POINTS ON ELLIPTIC CURVES OF RANK AT LEAST 3 (Analytic Number Theory : Arithmetic Properties of Transcendental Functions and their Applications)---92

　　　　日本大学理工学部 / U. Debrecen　　　平田典子 / Lality-Kovacs Tunde　(Hirata-Kohno,Noriko / Lality-Kovacs,Tunde)

10. Decomposition attack for the DLP of the Jacobian group of a curve over small characteristic field (Analytic Number Theory : Arithmetic Properties of Transcendental Functions and their Applications)---103

　　　　関東学院大学工学部　　　長尾孝一　(Nagao,Koh-ichi)

11. The multiple Dirichlet product and the multiple Dirichlet series (Analytic Number Theory : Arithmetic Properties of Transcendental Functions and their Applications)---115

　　　　名古屋大学多元数理科学研究科　　　小野塚友一　(ONOZUKA,TOMOKAZU)