Atkin and Swinnerton-Dyer congruences and noncongruence modular forms (Algebraic Number Theory and Related Topics 2012)

• Li, Wen-Ching Winnie

  Department of Mathematics, Pennsylvania State University・National Center for Theoretical Sciences, Mathematics Division, National Tsing Hua University

• Long, Ling

  Department of Mathematics, Louisiana State University

抄録

Atkin and Swinnerton-Dyer congruences are special congruence recursions satised by coefficients of noncongruence modular forms. These are in some sense p-adic analogues of Hecke recursion satised by classic Hecke eigenforms. They actually appeared in different contexts and sometimes can be obtained using the theory of formal groups. In this survey paper, we introduce the Atkin and Swinnerton-Dyer congruences, and discuss some recent progress on this topic.

"Algebraic Number Theory and Related Topics 2012". December 3～7, 2012. edited by Atsushi Shiho, Tadashi Ochiai and Noriyuki Otsubo. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

収録刊行物

• 数理解析研究所講究録別冊

  数理解析研究所講究録別冊 B51 269-299, 2014-10

  Research Institute for Mathematical Sciences, Kyoto University

キーワード

• 11F11
• 11F33
• 33C20

詳細情報

• CRID: 1050282810837010048
• NII論文ID: 110009911459
• NII書誌ID: AA12196120
• ISSN: 18816193
• HANDLE: 2433/232903
• 本文言語コード: en
• 資料種別: departmental bulletin paper
• データソース種別:
  • IRDB
  • CiNii Articles