## Analytic and Elementary Number Theory: A Tribute to Mathematical Legend Paul Erdos, Issues 1-2; Issue 1998This volume contains a collection of papers in Analytic and Elementary Number Theory in memory of Professor Paul Erdös, one of the greatest mathematicians of this century. Written by many leading researchers, the papers deal with the most recent advances in a wide variety of topics, including arithmetical functions, prime numbers, the Riemann zeta function, probabilistic number theory, properties of integer sequences, modular forms, partitions, and q-series. Audience: Researchers and students of number theory, analysis, combinatorics and modular forms will find this volume to be stimulating. |

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### Contents

II | 7 |

III | 21 |

IV | 39 |

V | 47 |

VI | 55 |

VII | 59 |

VIII | 67 |

IX | 153 |

XI | 185 |

XII | 201 |

XIII | 219 |

XIV | 225 |

XV | 247 |

XVI | 271 |

XVII | 283 |

X | 167 |

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1998 Kluwer Academic argument arithmetic progressions combinatorial completes the proof congruence constant convergence coprime Corollary define denote the number denote the set Department of Mathematics divisible divisors function estimate Ferrers graph finite set follows G.H. Hardy gives h.c. numbers implies inequality infinitely Lemma log log log2 log3 lower bound Math Mathematics Subject Classification modular form modulo multiplicative functions nombres nonnegative integers normal Note number of partitions number of prime number of solutions number of totients Number Theory obtain odd integers partition function Paul Erdos positive integer positive real number pre-image prime factors prime number prime number theorem proof of Lemma proof of Theorem Proposition Ramanujan representation residue class result Rogers-Ramanujan S-normal satisfying Section sequence set of integers shifted primes Sidon set sieve square squarefree number sufficiently large sumset Suppose Tenenbaum upper bound values Vk(x

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Page 2 - Ismail Department of Mathematics University of South Florida Tampa, FL 33620, USA...

Page 2 - Goldfeld Department of Mathematics Columbia University, New York, NY 10027, USA Professor Basil Gordon Department of Mathematics University of California Los Angeles, CA 90024, USA Professor Andrew Granville Department of Mathematics University of Georgia Athens, GA 30602, USA Professor Adolf Hildebrand Department of Mathematics University of illinois Urbana, IL...