𝐿-series and modular forms of half-integral weight

Hatcher, Rhonda L.

doi:10.1090/S0002-9939-1994-1233973-5

$L$-series and modular forms of half-integral weight
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Proc. Amer. Math. Soc. 122 (1994), 683-688 Request permission

Abstract:

Let f be a normalized Hecke eigenform of weight 2k, with k odd. The main result of this paper is an equation representing the value of $L(f,s)L(f \otimes \varepsilon ,s)$ at $s = k$ in terms of the Fourier coefficients of a modular form of half-integral weight.

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