## Topics in analytic number theory |

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### Contents

On the Distribution of the Zeros of the Riemann ZetaFunction | 28 |

Remarks on the Difference of Consecutive Numbers Prime to | 42 |

Some Solved and Unsolved Problems of Mine in Number Theory | 59 |

Copyright | |

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### Common terms and phrases

Acta Arith analytic number theory apply approximate functional equation argument arithmetic progressions assume automorphic Bombieri coefficients of cusp combinatorial sieve complex numbers congruence groups conjecture consecutive primes constant implied cusp forms defined denote depend Deshouillers Dirichlet polynomial divisor eigenvalues Eisenstein series Erdos error term exponent pairs finite Fourier coefficients Fouvry give Heath-Brown Hecke Hence holds Hooley integers Iwaniec Kloosterman sums Kuznetsov large sieve large sieve inequality Lemma linear Linnik log log log zl London Math lower bound mean-value theorem mod q modular forms modular group Montgomery multiplicative notation Note obtain Petersson conjecture Petersson formula Poincare series positive prime factors prime number theorem problem Proc proof result Riemann Hypothesis Riemann zeta-function right hand side satisfying second sum Selberg Selberg conjecture sequence sieve methods spectral square free sums of Kloosterman tion Titchmarsh trace formula trivial uniformly upper bound yields zeros of f(s zeta function