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2010 Fiscal Year Final Research Report

Class number and values of L-functions with cusp forms

Research Project

  • PDF
Project/Area Number 19740015
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionHiroshima University

Principal Investigator

ICHIHARA Yumiko  Hiroshima University, 理学部, 准教授 (80372689)

Project Period (FY) 2007 – 2010
Keywords整数論
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

    (14 results)

All 2011 2010 2009 2008

All Journal Article (6 results) (of which Peer Reviewed: 6 results) Presentation (8 results)

  • [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] Non-vanishing of the value of L-functions attached to primitive forms at a fixed point on the critical line2010

    • 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 theorem2009

    • 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 aspects2008

    • 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-functions2008

    • Author(s)
      Y.Ichihara, K.Matsumoto
    • Journal Title

      Kyushu J.Math. vol.62

      Pages: 201-215

    • 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 moment2009

    • 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

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Published: 2012-02-13   Modified: 2016-04-21  

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