On the Zeros of a Class of Dirichlet Series |
Contents
Introduction | 1 |
The number of zeros in a horizontal strip | 22 |
Some mean value theorems | 35 |
Copyright | |
2 other sections not shown
Common terms and phrases
² dt ² dy A₁ A₂ absolute convergence apply lemma arbitrary automorphic form chapter character mod q CLASS OF DIRICHLET class of functions conditions of theorem converges absolutely converges somewhere critical line cusp form deduce defined denote the number Dirichlet L-functions Dirichlet series Epstein zeta-functions estimate exists a positive finite order follows form of dimension form with signature Fourier function R(s functional equation Further G₂ Hecke Hence holds I₁ identically zero integral function interval Lekkerkerker mean value modular form modular group n(r₁ N₁(T No(T non-real zeros number of zeros O(log o₁ positive constant positive integer positive number possesses property principal value proof of theorem real coefficients real number relation represent an integral result Riemann hypothesis right half-plane satisfies sin² strip Suppose T₁ theorem 13 transformation valid y)-function μα Σαπ