Studies on symmetries for automorphic forms and Borcherds products

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400027
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Kyoto Sangyo University
• Principal Investigator: MURASE Atsushi 京都産業大学, 理学部, 教授 (40157772)
• Co-Investigator(Renkei-kenkyūsha): NARITA Hiroaki 熊本大学, 大学院自然科学研究科, 准教授 (70433315)
• Research Collaborator: SUGANO Takashi 金沢大学, 理工研究域数物科学系, 教授 (30183841) ; Bernhard Heim German University of Technology, 教授
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 保型形式 / 対称性 / Borcherds積

Outline of Final Research Achievements

We investigated on a condition for Siegel modular forms on congruence subgroups to have infinite product expansions. We define a notion of “generalized multiplicative symmetries” for a family of automorphic forms on various levels. We furthermore show that a family of automorphic forms with infinite product expansions satisfies generalized multiplicative symmetries. We also considered a similar problem for Jacobi forms and investigated a relation between infinite product expansions and generalized multiplicative symmetries.
We show that a Siegel modular form of degree 2 of level 1 which is simultaneously anSaito-Kurokawa lift and a Borchers product is a constant multiple of the Igusa modular form.

Free Research Field

整数論