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2023 年度 実績報告書

保型L関数の特殊値

研究課題

研究課題/領域番号 22KF0214
配分区分基金
研究機関京都大学

研究代表者

市野 篤史  京都大学, 理学研究科, 教授 (40347480)

研究分担者 CHEN SHIH-YU  京都大学, 理学研究科, 外国人特別研究員
研究期間 (年度) 2023-03-08 – 2024-03-31
キーワードSpecial L-values / Deligne's conjecture / Betti-Whittaker periods
研究実績の概要

In the literature, most known results on Deligne's conjecture or its automorphic analogue were obtained by cohomological interpretation of integral representation of the L-functions. The purpose of this research project is to investigate another approach to Deligne's conjecture. We consider ratios of Rankin-Selberg L-functions of algebraic automorphic representations of general linear groups. Under some regularity conditions, we prove that these ratios are algebraic at critical points. As applications, we prove new cases of Deligne's conjecture for symmetric power L-functions and tensor product L-functions of elliptic modular forms, which are previously known only for small degree. One technical difficulty in the proof of our main result is the non-vanishing of certain archimedean pairing. We extend the non-vanishing result of B. Sun to non-unitary cohomologically induced representations. The results of this research have been compiled into a paper and published as a preprint.

We also prove the trivialness of the relative period associated to a regular algebraic cuspidal automorphic representation of GL(2n) of orthogonal type. Together with the result of G. Harder and A. Raghuram, this implies the algebraicity of the ratios of successive critical L-values for GSpin(2n) x GL(n’). The results of this research were compiled into a paper and will be published by the International Mathematics Research Notices.

  • 研究成果

    (6件)

すべて 2024 2023

すべて 雑誌論文 (1件) (うち査読あり 1件) 学会発表 (5件) (うち国際学会 3件、 招待講演 5件)

  • [雑誌論文] On Petersson norms of generic cusp forms and special values of adjoint L-functions for GSp42023

    • 著者名/発表者名
      Chen Shih-Yu、Ichino Atsushi
    • 雑誌名

      American Journal of Mathematics

      巻: 145 ページ: 899~993

    • DOI

      10.1353/ajm.2023.a897499

    • 査読あり
  • [学会発表] Algebraicity of ratios of Rankin-Selberg L-functions2024

    • 著者名/発表者名
      Shih-Yu Chen
    • 学会等名
      NCTS-POSTECH-PMI Joint Workshop on Number Theory, POSCO Changeup Ground, Seoul, Korea
    • 国際学会 / 招待講演
  • [学会発表] Algebraicity of ratios of Rankin-Selberg L-functions2024

    • 著者名/発表者名
      Shih-Yu Chen
    • 学会等名
      Taiwanese Mathematical Society Annual Meeting, National Chengchi University, Taipei, Taiwan, ROC
    • 招待講演
  • [学会発表] Algebraicity of ratios of Rankin-Selberg L-functions2023

    • 著者名/発表者名
      Shih-Yu Chen
    • 学会等名
      北陸数論セミナー, 金沢大学サテライトプラザ
    • 招待講演
  • [学会発表] Algebraicity of ratios of Rankin-Selberg L-functions2023

    • 著者名/発表者名
      Shih-Yu Chen
    • 学会等名
      Pan Asian Number Theory Conference 2023, Harbin Institute of Technology, Harbin, PRC
    • 国際学会 / 招待講演
  • [学会発表] Algebraicity of ratios of Rankin-Selberg L-functions2023

    • 著者名/発表者名
      Shih-Yu Chen
    • 学会等名
      24th Autumn Workshop on Number Theory, Sapporo, Japan
    • 国際学会 / 招待講演

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公開日: 2024-12-25  

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