Periods of modular forms on τ0.N/ and products of Jacobi theta functions

Young Ju Choie; Yoon Kyung Park; Don Zagier

doi:10.4171/JEMS/864

Periods of modular forms on τ0.N/ and products of Jacobi theta functions

Young Ju Choie, Yoon Kyung Park, Don Zagier

School of Natural Sciences

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

8 Scopus citations

Abstract

Generalizing a result of [15] for modular forms of level one, we give a closed formula for the sum of all Hecke eigenforms on τ0.N/, multiplied by their odd period polynomials in two variables, as a single product of Jacobi theta series for any squarefree level N.We also show that for N D 2, 3 and 5 this formula completely determines the Fourier expansions of all Hecke eigenforms of all weights on τ0.N/.

Original language	English
Pages (from-to)	1379-1410
Number of pages	32
Journal	Journal of the European Mathematical Society
Volume	21
Issue number	5
DOIs	https://doi.org/10.4171/JEMS/864
State	Published - 2019

Keywords

Hecke eigenform
Jacobi theta series
Parabolic cohomology
Period
Rankin-Cohen brackets

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10.4171/JEMS/864

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abstract = "Generalizing a result of [15] for modular forms of level one, we give a closed formula for the sum of all Hecke eigenforms on τ0.N/, multiplied by their odd period polynomials in two variables, as a single product of Jacobi theta series for any squarefree level N.We also show that for N D 2, 3 and 5 this formula completely determines the Fourier expansions of all Hecke eigenforms of all weights on τ0.N/.",

keywords = "Hecke eigenform, Jacobi theta series, Parabolic cohomology, Period, Rankin-Cohen brackets",

author = "Choie, \{Young Ju\} and \{Kyung Park\}, Yoon and Don Zagier",

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AU - Kyung Park, Yoon

AU - Zagier, Don

N1 - Publisher Copyright: © European Mathematical Society 2019.

PY - 2019

Y1 - 2019

N2 - Generalizing a result of [15] for modular forms of level one, we give a closed formula for the sum of all Hecke eigenforms on τ0.N/, multiplied by their odd period polynomials in two variables, as a single product of Jacobi theta series for any squarefree level N.We also show that for N D 2, 3 and 5 this formula completely determines the Fourier expansions of all Hecke eigenforms of all weights on τ0.N/.

AB - Generalizing a result of [15] for modular forms of level one, we give a closed formula for the sum of all Hecke eigenforms on τ0.N/, multiplied by their odd period polynomials in two variables, as a single product of Jacobi theta series for any squarefree level N.We also show that for N D 2, 3 and 5 this formula completely determines the Fourier expansions of all Hecke eigenforms of all weights on τ0.N/.

KW - Hecke eigenform

KW - Jacobi theta series

KW - Parabolic cohomology

KW - Period

KW - Rankin-Cohen brackets

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JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

IS - 5

ER -

Periods of modular forms on τ0.N/ and products of Jacobi theta functions

Abstract

Keywords

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