Analytic Number Theory

1. Front Matter

   Pages i-viii

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2. q-Trinomial Coefficients and Rogers-Ramanujan Type Identities

   • George E. Andrews

   Pages 1-11

3. Evaluations of Selberg Character Sums

   • Julie Autuore, Ronald Evans

   Pages 13-21

4. Oscillations of Quadratic L-Functions

   • R. C. Baker, Hugh L. Montgomery

   Pages 23-40

5. Elementary Proof of a Theorem of Bateman

   • Michel Balazard, Abdelhakim Smati

   Pages 41-46

6. The Prime k-Tuplets Conjecture on Average

   • Antal Balog

   Pages 47-75

7. On Arithmetic Functions Involving Consecutive Divisors

   • Antal Balog, Paul Erdös, G. Tenenbaum

   Pages 77-90

8. Small Zeros of Quadratic Forms Modulo p, II

   • Todd Cochrane

   Pages 91-94

9. Zeros of Derivatives Of the Riemann Zeta-Function Near the Critical Line

   • J. B. Conrey, A. Ghosh

   Pages 95-110

10. On some Exponential Sums

    • H. Daboussi

    Pages 111-118

11. On the Integers n for which Ω(n)=k

    • H. Delange

    Pages 119-132

12. A Boundary Value Problem for a Pair of Differential Delay Equations Related to Sieve Theory, I

    • H. Diamond, H. Halberstam, H.-E. Richert

    Pages 133-157

13. Some Remarks about Multiplicative Functions of Modulus < 1

    • P. D. T. A. Elliott

    Pages 159-164

14. On the Normal Behavior of the Iterates Of some Arithmetic Functions

    • Paul Erdös, Andew Granvilie, Carl Pomerance, Claudia Spiro

    Pages 165-204

15. On the Number of Partitions of n Without a Given Subsum, II

    • P. Erdös, J. L. Nicolas, A. Sárközy

    Pages 205-234

16. On Gaps between Squarefree Numbers

    • Michael Filaseta, Ognian Trifonov

    Pages 235-253

17. Some Arithmetical Semigroups

    • A. S. Fraenkel, H. Porta, K. B. Stolarsky

    Pages 255-264

18. Norms in Arithmetic Progressions

    • J. B. Friedlander, H. Iwaniec

    Pages 265-268

19. Lower Bounds for Least Quadratic Non-Residues

    • S. W. Graham, C. J. Ringrose

    Pages 269-309

20. Some Conjectures in Analytic Number Theory And their Connection With Fermat’s Last Theorem

    • Andrew Granville

    Pages 311-326

On April 25-27, 1989, over a hundred mathematicians, including eleven from abroad, gathered at the University of Illinois Conference Center at Allerton Park for a major conference on analytic number theory. The occa­ sion marked the seventieth birthday and impending (official) retirement of Paul T. Bateman, a prominent number theorist and member of the mathe­ matics faculty at the University of Illinois for almost forty years. For fifteen of these years, he served as head of the mathematics department. The conference featured a total of fifty-four talks, including ten in­ vited lectures by H. Delange, P. Erdos, H. Iwaniec, M. Knopp, M. Mendes France, H. L. Montgomery, C. Pomerance, W. Schmidt, H. Stark, and R. C. Vaughan. This volume represents the contents of thirty of these talks as well as two further contributions. The papers span a wide range of topics in number theory, with a majority in analytic number theory.

• analytic number theory
• number theory
• prime number

• Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, USA

  Bruce C. Berndt, Harold G. Diamond, Heini Halberstam, Adolf Hildebrand

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