Meromorphic analogues of modular forms generating the kernel of Shintani's lift

Paloma Bengoechea

doi:10.4310/MRL.2015.v22.n2.a2

Meromorphic analogues of modular forms generating the kernel of Shintani's lift

Paloma Bengoechea

Mathematics

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

Abstract

We study the meromorphic modular forms defined as sums of -k (k>1) powers of integral quadratic polynomials with negative discriminant. These functions can be viewed as meromorphic analogues of the holomorphic modular forms defined in the same way with positive discriminant, first investigated by Zagier in connection with the Doi-Naganuma map and then by Kohnen and Zagier in connection with the Shimura-Shintani lifts. We compute the Fourier coefficients of these meromorphic modular forms and we show that they split into the sum of a meromorphic modular form with computable algebraic Fourier coefficients and a holomorphic cusp form.

Original language	Undefined/Unknown
Pages (from-to)	337-352
Number of pages	14
Journal	Mathematical Research Letters
Volume	22
Issue number	2
DOIs	https://doi.org/10.4310/MRL.2015.v22.n2.a2
Publication status	Published - 2015

Bibliographical note

This is an author produced version of a paper accepted for publication in Mathematical Research Letters. Uploaded in accordance with the publisher's self-archiving policy.

Keywords

math.NT

Access to Document

10.4310/MRL.2015.v22.n2.a2

1304.5653v2
This is an author produced version of a paper accepted for publication in Mathematical Research Letters. Uploaded in accordance with the publisher's self-archiving policy.
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Cite this

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