Analytic and Elementary Number Theory

1. Front Matter

   Pages 1-4

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2. Editorial

   • Krishnaswami Alladi

   Pages 5-6

3. Euler’s Function in Residue Classes

   • Thomas Dence, Carl Pomerance

   Pages 7-20

4. Partition Identities Involving Gaps and Weights, II

   • Krishnaswami Alladi

   Pages 21-37

5. The Voronoi Identity via the Laplace Transform

   • Aleksandar Ivić

   Pages 39-45

6. The Residue of p(N) Modulo Small Primes

   • Ken Ono

   Pages 47-54

7. A Small Maximal Sidon Set

   • Imre Z. Ruzsa

   Pages 55-58

8. Sums and Products from a Finite Set of Real Numbers

   • Kevin Ford

   Pages 59-66

9. The Distribution of Totients

   • Kevin Ford

   Pages 67-151

10. A Mean-Value Theorem for Multiplicative Functions on the Set of Shifted Primes

    • Karl-Heinz Indlekofer, Nikolai M. Timofeev

    Pages 153-165

11. Entiers Lexicographiques

    • André Stef, Gérald Tenenbaum

    Pages 167-184

12. The Berry-Esseen Bound in the Theory of Random Permutations

    • E. Manstavičius

    Pages 185-199

13. Products of Shifted Primes. Multiplicative Analogues of Goldbach’s Problems, II

    • P. D. T. A. Elliott

    Pages 201-217

14. On Products of Shifted Primes

    • P. Berrizbeitia, P. D. T. A. Elliott

    Pages 219-223

15. On Large Values of the Divisor Function

    • P. Erdős, J.-L. Nicolas, A. Sárközy

    Pages 225-245

16. Some New Old-Fashioned Modular Identities

    • Paul T. Bateman, Marvin I. Knopp

    Pages 247-269

17. Linear Forms in Finite Sets of Integers

    • Shu-Ping Han, Christoph Kirfel, Melvyn B. Nathanson

    Pages 271-281

18. A Binary Additive Problem of Erdős and the Order of 2 mod p ²

    • Andrew Granville, K. Soundararajan

    Pages 283-298

This 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.

• Distribution
• Maximum
• Modular form
• Prime
• Prime number
• Riemann zeta function
• number theory
• combinatorics

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