Study of Eisenstein series and related Dirichlet series

2012 Fiscal Year Final Research Report

• Project/Area Number: 23740021
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: The University of Tokushima
• Principal Investigator: MIZUNO Yoshinori 徳島大学, 大学院・ソシオテクノサイエンス研究部, 准教授 (30546388)
• Project Period (FY): 2011 – 2012
• Keywords: アイゼンシュタイン級数 / ケッヒャー・マース級数 / フーリエ係数 / 類数 / L関数の特殊値 / ディリクレ級数 / 逆定理 / p 進アイゼンシュタイン級数

Research Abstract

We study several Dirichlet series associated to modular forms of degree one or two. First, we discovered a new application of Koecher-Maass series of Siegel modular forms. Namely we got a new proof of recent result of Kohnen and Martin on a characterization of degree 2 Siegel cusp forms by the growth of their Fourier coefficients. Our main tools are Koecher-Maass series. Second, we gave some new construction of holomorphic kernel functions of modular L-functions. Using this, we can compute special L-values numericallyrather easily .

Research Products

• [Journal Article] Spectral theory on 3-dimensional hyperbolic space and Hermitian modular forms (2012)
  • Author(s): Roland Matthes, Yoshinori Mizuno
  • Journal Title: Forum Mathematicum Pages: 掲載決定
  • Peer Reviewed
• [Journal Article] Regularized theta lift and formulas ofKatok-Sarnak type (2012)
  • Author(s): Roland Matthes, Yoshinori Mizuno
  • Journal Title: Forum Mathematicum Volume: 85巻 Pages: 455-471
  • DOI: doi:10.1515/FORM.2011.103
  • Peer Reviewed
• [Journal Article] Dirichlet series associated with square of class numbers of binary quadratic forms (2012)
  • Author(s): Yoshinori Mizuno
  • Journal Title: Mathematische Zeitschrift Volume: 132巻 Pages: 837-860
  • DOI: doi:10.1007/s00209-012-0979-y
  • Peer Reviewed
• [Journal Article] On p-adic Hermitian-Eisenstein series and a p-adic Siegel cusp form (2012)
  • Author(s): Toshiyuki Kikuta, Yoshinori Mizuno
  • Journal Title: Journal of Number Theory Volume: 132巻 Pages: 1946-1961
  • DOI: doi:10.1016/j.jnt.2012.03.003
  • Peer Reviewed
• [Journal Article] Linear dependence of certain L-values of half-integral weight modular forms (2012)
  • Author(s): Hidenori Katsurada, Yoshinori Mizuno
  • Journal Title: J. London Math. Soc (2) Volume: 85巻 Pages: 455-471
  • DOI: doi:10.1112/jlms/jdr057
  • Peer Reviewed
• [Journal Article] Dirichlet series associated with squareof class numbers of binary quadratic forms (2012)
  • Author(s): Yoshinori Mizuno
  • Journal Title: 早稲田大学整数論研究集会2012報告集 Pages: 13-26
• [Journal Article] Dirichlet series associated with squareof the class numbers (2011)
  • Author(s): Yoshinori Mizuno
  • Journal Title: 京都大学数理解析研究所講究録 No. 1767 「保型形式と関連する跡公式, ゼータ関数の研究」 Pages: 161-170
  • URL: http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1767-16.pdf
• [Presentation] On characterization of Siegel cusp forms of degree 2 by the Hecke bound (2012)
  • Author(s): 水野義紀
  • Organizer: Workshop on modular forms
  • Place of Presentation: 九州大学(福岡県)
  • Year and Date: 2012-09-28
• [Presentation] Dirichlet series associated with square of class numbers of binary quadratic forms (2012)
  • Author(s): 水野義紀
  • Organizer: 早稲田大学整数論研究集会 2012
  • Place of Presentation: 早稲田大学(東京都)
  • Year and Date: 2012-03-19
• [Presentation] Dirichlet series associated with square of class numbers of binary quadratic forms, 「 L-functions of automorphic forms and related problems」 (2012)
  • Author(s): 水野義紀
  • Place of Presentation: 東京大学(東京都)
  • Year and Date: 2012-03-11
• [Presentation] 数論的古典解析の話題から (2012)
  • Author(s): 水野義紀
  • Organizer: 保型形式ミニ研究集会
  • Place of Presentation: 近畿大学(大阪府)
  • Year and Date: 2012-03-03
• [Presentation] 第5回ゼータ若手研究集会 (2012)
  • Author(s): 水野義紀
  • Organizer: 二元二次形式の類数の自乗に付随するディリクレ級数について
  • Place of Presentation: 名古屋大学(愛知県)
  • Year and Date: 2012-02-11
• [Remarks] 京都大学・集中講義「ケッヒャー・マース級数と今井の逆定理」2012 年 11 月 26 日～30 日, 京都大学
• [Remarks] 2012 年 11 月 26 日～30 日, 京都大学
• [Remarks]
  • URL: http://pub2.db.tokushima-u.ac.jp/ERD/person/186508/profile-ja.html