Remarks on Kohnen-Zagier's paper concerning Fourier coefficients of modular forms of half integral weight
Let \(\psi\) denote Shimura's correspondence between elliptic modular forms of half-integral and even weight. Consider a Hecke eigenform \(f\) in Kohnen's ``+''-space \(S^ +_{k+ 1/2}(4)\) with Fourier coefficients \(a(n)\), \(n\geq 1\). \textit{W. Kohnen} and \textit{D. Zagier} [Invent. Math. 64, 175-198 (1981; Zbl 0468.10015)] explicitly determined the proportionality of \(a(n)^ 2\) for square free \(n\) with a special value of the zeta function associated with \(\psi(f)\). In the paper under review the author announces the analogous result for a Hecke eigenform \(f\in S_{k+1/2} (4N)\) resp. \(f\in S_{k+1/2} (4N,\chi_ N)\) such that \(\psi(f)\) is a primitive form in \(S_{2k} (2N)\).
scientific article; zbMATH DE number 597326