Class number and values of L-functions with cusp forms

• Project/Area Number: 19740015
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Hiroshima University
• Principal Investigator: ICHIHARA Yumiko Hiroshima University, 理学部, 准教授 (80372689)
• Project Period (FY): 2007 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥4,020,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥720,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2007: ¥900,000 (Direct Cost: ¥900,000)
• Keywords: 整数論 / 数論 / non-vanishing / L関数 / 特殊値 / 蘭数 / ジーゲル・竜沢の定理

Research Abstract

I studied the space of cusp forms whose level is prime power and obtained an orthogonal basis of space of old forms. It's yielded the number of the new forms which L-function does not vanish.

Research Products

• [Journal Article] The first moment of L-functions of primitive forms on $\Gamma_0(p^{\alpha})$ and a basis of old forms. (2011)
  • Author(s): Y.Ichihara
  • Journal Title: Journal of Number Theory vol.131, no.2 Pages: 343-362
  • Peer Reviewed
• [Journal Article] The first moment of L-functions of primitive forms on $￥Gamma_0(p^{￥alpha})$ and a basis of old forms (2011)
  • Author(s): Yumiko Ichihara
  • Journal Title: Journal of Number Theory Volume: 131 Pages: 343-362
  • Peer Reviewed
• [Journal Article] Non-vanishing of the value of L-functions attached to primitive forms at a fixed point on the critical line (2010)
  • Author(s): Y.Ichihara
  • Journal Title: 数理解析研究所講究録 1710 Pages: 29-41
  • Peer Reviewed
• [Journal Article] 保型L関数のnon-vanishing theorem (2009)
  • Author(s): Y.Ichihara
  • Journal Title: 第二回数論女性の集まり報告集 Pages: 1-5
  • Peer Reviewed
• [Journal Article] Siegel-Tatuzawaの定理について (2008)
  • Author(s): Y.Ichihara
  • Journal Title: 第一回数論女性の集まり報告集 Pages: 1-9
  • Peer Reviewed
• [Journal Article] Estimates of a certain sum involving coefficients of cuspforms in weight and level aspects (2008)
  • Author(s): Y.Ichihara
  • Journal Title: Lithuanian Math.J. vol.48, no.2 Pages: 188-202
  • Peer Reviewed
• [Journal Article] On the Siegel-Tatuzawa theorem for a class of L-functions (2008)
  • Author(s): Y.Ichihara, K.Matsumoto
  • Journal Title: Kyushu J.Math. vol.62 Pages: 201-215
  • NAID: 110006648022
  • Peer Reviewed
• [Journal Article] On the Siegel -Tatuzawa theorem for a class of L-functions (2008)
  • Author(s): Yumiko Ichihara
  • Journal Title: Kyushu Journal Mathematics Vol.62no.1 Pages: 201-215
  • NAID: 110006648022
  • Peer Reviewed
• [Journal Article] Estimates of a certain sum involving coefficents of cusp forms in weight and level aspects (2008)
  • Author(s): Yumiko Ichihara
  • Journal Title: Lithuanian Mathematial Journal Vol.48
  • Peer Reviewed
• [Presentation] Non-vanishing of the automorphic L-functions at the pointon the critical line. (2010)
  • Author(s): Y.Ichihara
  • Organizer: The 15th. Joint Workshop on Numver Theory between Japan and Taiwan
  • Place of Presentation: (in Waseda University, Organizers : YU Jing(National Taiwan Univ.), KOMATSUKei-ichi (Waseda Univ.), HASHIMOTO Ki-ichiro (Waseda Univ.), UMEGAKIAtsuki(WIAS)
  • Year and Date: 2010-03-19
• [Presentation] Non-vanishing of the value of the L-functions attached to primitive forms on the critical line. (2009)
  • Author(s): Y.Ichihara
  • Organizer: 研究集会「解析整数およびその周辺の諸問題」(研究代表者:津村博文)
  • Place of Presentation: 京都大学数理解析研究所,
  • Year and Date: 2009-10-14
• [Presentation] Cusp formに付随するL関数の1/2+itにおけるfirst moment (2009)
  • Author(s): Y.Ichihara
  • Organizer: 日本数学会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-24
• [Presentation] The first moment of the value of automorphic L-functions over primitive forms on the critical line. (2009)
  • Author(s): Y.Ichihara
  • Organizer: CONFERENCE IN NUMBER THEORY
  • Place of Presentation: Carleton University, CANADA,Organizers : Saban Alaca, Gary Walsh, Kenneth Williams
  • Year and Date: 2009-06-27
• [Presentation] 保型L関数のnon-vanishing theorem. (2009)
  • Author(s): Y.Ichihara
  • Organizer: 研究集会「第二回数論女性の集まり」
  • Place of Presentation: (早稲田大学, 世話人:広中由美子, 太田香, 川内真由美, 市原由美子)
  • Year and Date: 2009-05-09
• [Presentation] primitive formに対する保型L関数のcritical line上の点におけるfirst moment. (2009)
  • Author(s): Y.Ichihara
  • Organizer: 研究集会「第2回ゼータ若手研究集会」
  • Place of Presentation: 名古屋大学, 代表者:佐々木義卓
  • Year and Date: 2009-02-21
• [Presentation] Siegel-Tatuzawaの定理について (2008)
  • Author(s): Y.Ichihara
  • Organizer: 研究集会「第一回数論女性の集まり」
  • Place of Presentation: 於早稲田大学, 世話人:広中由美子, 太田香, 大溪幸子, 市原由美子)
  • Year and Date: 2008-05-17
• [Presentation] Estimates of a certain sum involving coefficients of cusp forms in weight and level aspects. (2008)
  • Author(s): Y.Ichihara
  • Organizer: French-Japanese Winter School on Zeta and L-functions
  • Place of Presentation: in Miura-kaigan, Organizers : K.Matsumoto and H.Tsumura
  • Year and Date: 2008-01-08