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2016 Fiscal Year Final Research Report

Studies on symmetries for automorphic forms and Borcherds products

Research Project

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Project/Area Number 26400027
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionKyoto 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

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Published: 2018-03-22  

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