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Zeta-functions of harmonic theta-series and prime numbers

Zeta-functions of harmonic theta-series and prime numbers

The problem of finding Euler product expansions is treated for zeta-functions of modular forms in one variable that are presented by harmonic theta-series. On the basis of the author’s formulas obtained earlier for the action of the Hecke operators on harmonic theta-functions, Euler product expansions are obtained for eigenfunctions of …