Ternary quadratic forms and half-integral weight modular forms

DOI10.1112/S1461157012001155zbMATH Open1294.11060arXiv1609.07218OpenAlexW2964094567MaRDI QIDQ5169650

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Publication date: 11 July 2014

Published in: (Search for Journal in Brave)

Abstract: Let $k$ be a positive integer such that $kequiv3mod4$, and let $N$ be a positive square-free integer. In this paper, we compute a basis for the two-dimensional subspace $S_{frack2}(Gamm{a}_0(4N),F)$ of half-integral weight modular forms associated, via the Shimura correspondence, to a newform $Fin{S}_{k-1}(Gamm{a}_0(N))$, which satisfies $L(F,frac12)eq0$. This is accomplished by using a result of Waldspurger, which allows one to produce a basis for the forms that correspond to a given $F$ via local considerations, once a form in the Kohnen space has been determined

Full work available at URL: https://arxiv.org/abs/1609.07218

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