Research Article

The square mean of Dirichlet series associated with cusp forms

Anton Gooda1

a1 Forschungsinstitut für Mathematik, ETH-Zentrum, CH-8092 Zürich, Switzerland

Let

S0025579300012377_eqnU1

be a cusp form of even integral weight k > 2 for the full modular group. Then the Dirichlet series

S0025579300012377_eqnU2

is absolutely convergent for σ > ½(k + 1). Hecke showed that LF is an entire function of s satisfying the functional equation

S0025579300012377_eqn1

(Received September 14 1981)

Key Words:

  • 10D12: NUMBER THEORY; Theory of modular forms; Modular forms, one variable