## Number Theory, Volume 1Containing contributions from leading mathematicians worldwide, this two-volume set gives a comprehensive picture of current research in Number Theory.The topics include:bull; elementary number theorybull; sequences of integersbull; additive and multiplicative number theorybull; exponential and character sumsbull; zeta and L-functionsbull; uniform distributionbull; diophantine approximationbull; geometry of numbersbull; transcendental numbersbull; polynomialsbull; finite fieldsbull; algebraic number theorybull; arithmetic algebraic geometrybull; computational number theory. |

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### Contents

Volume | 5 |

T A ELLIOTT Applications of elementary | 35 |

P ERDOS and A IVIC The distribution of values | 45 |

Copyright | |

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### Common terms and phrases

1+iA Acta additive functions algebraic Alog Arith arithmetic functions Artin L-function asymptotic basis asymptotic formula basis of order Benford's law BUDAPEST BUDAPEST HUNGARY COLLOQUIA MATHEMATICA SOCIETATIS completes the proof condition consecutive integers consider constant convergence COROLLARY coset defined denote the number Dirichlet character Dirichlet series divisor function equation Erdos estimate exists exponential sums finite fixed function f Hence holds IA-AI implies inequality integer interval Iwaniec JANOS BOLYAI JANOS BOLYAI 5I L-functions Lemma log log MATHEMATICA SOCIETATIS JANOS minimal asymptotic basis Mirsky multiplicative functions natural numbers nullpotent number of solutions number theory obtain polynomial positive integers prime factors prime number prime number theorem principal solution problem PROOF OF THEOREM proved R-additive real number REMARK result Riemann zeta function satisfying sequence SOCIETATIS JANOS BOLYAI squarefree squarefull strongly additive subgroup sufficiently large summand summation suppose term THEOREM 2.1 tion topology vectors x-y<nSx zero