1999 年度実績報告書

ゼータ関数,L関数の挙動とその整数論的意味

研究課題

研究課題/領域番号	09440009
研究機関	名古屋大学
研究代表者	松本耕二名古屋大学, 大学院・多元数理科学研究科, 助教授 (60192754)
研究分担者	伊藤博名古屋大学, 大学院・多元数理科学研究科, 教授 (30168372) 谷川好男名古屋大学, 大学院・多元数理科学研究科, 助教授 (50109261) 北岡良之名古屋大学, 大学院・多元数理科学研究科, 教授 (40022686) 桂田昌紀慶応大学, 経済学部, 助教授 (90224485) 秋山茂樹新潟大学, 理学部, 助教授 (60212445)
キーワード	Riemannゼータ関数 / Dirichlet L関数 / Voronoiの公式 / 約数問題 / 二乗平均 / 漸近展開 / Rankin-Selberg L関数
研究概要	約数問題(Δa(x)の評価)とRiemannゼータ関数の二乗平均の残余項Eσ(T)の評価との間には強いアナロジーが成立し,それぞれVoronoiの公式とAtkinsonの公式が重要な研究手段である。これについて, 1.短区間におけるΔa(x)やEσ(T)の差の二乗平均値公式を,それぞれVoronoi公式,Atkinson公式を用いてもとめ,さらにゼータ関数の二乗の近似関数等式の残余項についても類似の結果を証明した。 2.指標付きの場合への拡張をすすめた。 3.Rankin-SelbergのL関数の係数のRiesz和に対するVoronoi型公式を証明し,二乗平均値定理を示した。 4.Mellin-Barnes型積分表示を用いる手法を開発し,解析接続及び漸近展開を求める時に有用な手段であることを立証した。

研究成果
(17件)

すべてその他

すべて文献書誌 (17件)

[文献書誌] T.Hattori,K.Matsumoto: "A limit theorem for Bohr-Jessen's probability measures of the Riemann zeta-function"J.Reine Angew.Math. 507. 219-232 (1999)
[文献書誌] K.Matsumoto,Y.Tanigawa: "On the zeros of higher derivatives of Hardy's Ζ-function"J.Number Theory. 75. 262-278 (1999)
[文献書誌] A.Ivic,K.Matsumoto,Y.Tanigawa: "On Riesz means of the eoefficients of the Rankin-Selberg series"Math.Proc.Cambridge Phil.Soc.. 127. 117-131 (1999)
[文献書誌] M.Katsurada,K.Matsumoto: "A weighted integral approach to the mean square of Dirichlet L-functions""Number Theory and its Applications",Kluwer. 199-229 (1999)
[文献書誌] K.Matsumoto: "Recent developments in the mean square theory of the Riemann zeta and other zeta-functions""Number Theory" Hindustan. (to appear).
[文献書誌] A.Laurineikas,K.Matsumoto: "A joint universality and the functional independence for Lerch zeta-functions"Nagoya Math. J.. (to appear).
[文献書誌] Y.Kitaoka: "Finite arithmetic subgroups of GLn VI."Contemp.Math.. 249. 63-71 (1999)
[文献書誌] S.Akiyama,Y.Tanigawa: "Calculation of values of L-functions associated to elliptic curves"Math.Comput.. 68. 1201-1231 (1999)
[文献書誌] I.Kiuchi,Y.Tanigawa: "The mean value theorem of the Riemann zeta-function in the critical strip for short intervals""Number Theory and its Applications" Kluwer. 231-240 (1999)
[文献書誌] I.Kiuchi,Y.Tanigawa: "A mean value theorem of the approximate functional equation of ζ(s)^2 for short intervals"J.Ramanujan Math.Soc.. (to appear).
[文献書誌] S.Egami: "On the mean square of Hecke L-functions associated to holomorphic cusp forms""Number Theory and its Applications" Kluwer. 101-110 (1999)
[文献書誌] I.Kiuchi: "On the mean value formula for the non-symmetric form of the approximate functional equation of ζ^2(s) in the critical strip"Publ.Math.Debrecen. (to appear).
[文献書誌] M.Amou,M.Katsurada: "Irrationality results for values of generalized Tschakaloft series"J.Number Theory. 77. 155-169 (1999)
[文献書誌] M.Katsurada: "Rapidly convergent series representations for ζ(2n+1) and their x-analogue"Acta Arith.. 90. 79-89 (1999)
[文献書誌] S.Kanemitsu,M.Katsurada,M.Yoshimoto: "On the Hurwitz-Lerch zeta-function"Aequationes Math.. (to appear).
[文献書誌] S.Akiyama: "Self Affine tiling and Pisot numeration system""Number Theory and its Applications" Kluwer. 7-17 (1999)
[文献書誌] S.Akiyama,J.Thuswaldner: "Topological properties of two-dimensional number systems"J.Th.Nomb.Bordeaux. (to appear).

1999 年度 実績報告書

ゼータ関数,L関数の挙動とその整数論的意味

研究代表者

松本 耕二 名古屋大学, 大学院・多元数理科学研究科, 助教授 (60192754)

研究成果

[文献書誌] T.Hattori,K.Matsumoto: "A limit theorem for Bohr-Jessen's probability measures of the Riemann zeta-function"J.Reine Angew.Math. 507. 219-232 (1999)

[文献書誌] K.Matsumoto,Y.Tanigawa: "On the zeros of higher derivatives of Hardy's Ζ-function"J.Number Theory. 75. 262-278 (1999)

[文献書誌] A.Ivic,K.Matsumoto,Y.Tanigawa: "On Riesz means of the eoefficients of the Rankin-Selberg series"Math.Proc.Cambridge Phil.Soc.. 127. 117-131 (1999)

[文献書誌] M.Katsurada,K.Matsumoto: "A weighted integral approach to the mean square of Dirichlet L-functions""Number Theory and its Applications",Kluwer. 199-229 (1999)

[文献書誌] K.Matsumoto: "Recent developments in the mean square theory of the Riemann zeta and other zeta-functions""Number Theory" Hindustan. (to appear).

[文献書誌] A.Laurineikas,K.Matsumoto: "A joint universality and the functional independence for Lerch zeta-functions"Nagoya Math. J.. (to appear).

[文献書誌] Y.Kitaoka: "Finite arithmetic subgroups of GLn VI."Contemp.Math.. 249. 63-71 (1999)

[文献書誌] S.Akiyama,Y.Tanigawa: "Calculation of values of L-functions associated to elliptic curves"Math.Comput.. 68. 1201-1231 (1999)

[文献書誌] I.Kiuchi,Y.Tanigawa: "The mean value theorem of the Riemann zeta-function in the critical strip for short intervals""Number Theory and its Applications" Kluwer. 231-240 (1999)

[文献書誌] I.Kiuchi,Y.Tanigawa: "A mean value theorem of the approximate functional equation of ζ(s)^2 for short intervals"J.Ramanujan Math.Soc.. (to appear).

[文献書誌] S.Egami: "On the mean square of Hecke L-functions associated to holomorphic cusp forms""Number Theory and its Applications" Kluwer. 101-110 (1999)

[文献書誌] I.Kiuchi: "On the mean value formula for the non-symmetric form of the approximate functional equation of ζ^2(s) in the critical strip"Publ.Math.Debrecen. (to appear).

[文献書誌] M.Amou,M.Katsurada: "Irrationality results for values of generalized Tschakaloft series"J.Number Theory. 77. 155-169 (1999)

[文献書誌] M.Katsurada: "Rapidly convergent series representations for ζ(2n+1) and their x-analogue"Acta Arith.. 90. 79-89 (1999)

[文献書誌] S.Kanemitsu,M.Katsurada,M.Yoshimoto: "On the Hurwitz-Lerch zeta-function"Aequationes Math.. (to appear).

[文献書誌] S.Akiyama: "Self Affine tiling and Pisot numeration system""Number Theory and its Applications" Kluwer. 7-17 (1999)

[文献書誌] S.Akiyama,J.Thuswaldner: "Topological properties of two-dimensional number systems"J.Th.Nomb.Bordeaux. (to appear).

1999 年度実績報告書

松本耕二名古屋大学, 大学院・多元数理科学研究科, 助教授 (60192754)