Eigenform product identities for Hilbert modular forms

Kirti Joshi; Yichao Zhang

doi:10.1007/s00209-018-2214-y

Eigenform product identities for Hilbert modular forms

Kirti Joshi, Yichao Zhang

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We prove that amongst all real quadratic fields and all spaces of Hilbert modular forms of full level and of weight 2 or greater, the product of two Hecke eigenforms is not a Hecke eigenform except for finitely many real quadratic fields and finitely many weights. We show that for Q(5) there are exactly two such identities.

Original language	English (US)
Pages (from-to)	1161-1179
Number of pages	19
Journal	Mathematische Zeitschrift
Volume	293
Issue number	3-4
DOIs	https://doi.org/10.1007/s00209-018-2214-y
State	Published - Dec 1 2019

Keywords

Hecke eigenform
Hilbert modular form
Product identity

ASJC Scopus subject areas

General Mathematics

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10.1007/s00209-018-2214-y

Cite this

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abstract = "We prove that amongst all real quadratic fields and all spaces of Hilbert modular forms of full level and of weight 2 or greater, the product of two Hecke eigenforms is not a Hecke eigenform except for finitely many real quadratic fields and finitely many weights. We show that for Q(5) there are exactly two such identities.",

keywords = "Hecke eigenform, Hilbert modular form, Product identity",

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AB - We prove that amongst all real quadratic fields and all spaces of Hilbert modular forms of full level and of weight 2 or greater, the product of two Hecke eigenforms is not a Hecke eigenform except for finitely many real quadratic fields and finitely many weights. We show that for Q(5) there are exactly two such identities.

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KW - Hilbert modular form

KW - Product identity

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Eigenform product identities for Hilbert modular forms

Abstract

Keywords

ASJC Scopus subject areas

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