Hecke operators on modular forms of half-integral weight
Copyright policy )Hecke operators on modular forms of half-integral weight
In the paper [Arch. Math. 32, 158-165 (1979; Zbl 0407.10022)] \textit{Hong- Jen Hsiao} and \textit{Hong-Chang Lee} have proved that the Dirichlet series associated with a modular form f of integral weight for the full modular group has an Euler product expansion if and only if f is an eigenfunction for finitely many explicitly given Hecke operators. In this paper the same problem has been considered for W. Kohnen's \(``+\) space'' of modular forms of half-integral weight for the congruence subgroup \(\Gamma _ 0(4)\). The methods used in this paper are completely different and simpler and also reduce very much the number of conditions given in the above paper for the modular forms over the full modular group.
Euler product expansion, Hecke operators, congruence subgroup, Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, Automorphic forms, one variable, modular forms of half-integral weight, Dirichlet series, Holomorphic modular forms of integral weight
Euler product expansion, Hecke operators, congruence subgroup, Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, Automorphic forms, one variable, modular forms of half-integral weight, Dirichlet series, Holomorphic modular forms of integral weight
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