## On the Zeros of a Class of Dirichlet Series |

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### 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

absolute convergence analytic continuation apply lemma arithmetical function automorphic form behaviour chapter character mod q class of functions complex number conditions of theorem contain a zero converges absolutely converges somewhere critical line cusp form deduce defined denote the number dimension x Dirichlet series domain e.g. Titchmarsh Epstein zeta-functions estimate exists a positive finite order form of dimension form with signature fulfills condition function p(s functional equation Further given signature Hecke Hence holds hypothesis identically zero integral function interval Lekkerkerker Let h Let p(s mean value modular form modular group non-real zeros number of zeros 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 strip Suppose that p(s theorem 13 transformation valid y)-function zeros of p(s оо ст