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

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JournalMathematical Research Letters
DatePublished - 2015
Issue number2
Volume22
Number of pages14
Pages (from-to)337-352
Original languageUndefined/Unknown

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.

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  • math.NT

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