Analytic Number Theory

1. Front Matter

   Pages i-xiv

   PDF

2. Weighted partition identities and applications

   • Krishnaswami Alladi

   Pages 1-15

3. Rogers-Ramanujan polynomials for modulus 6

   • George E. Andrews

   Pages 17-30

4. On subset-sum-distinct sequences

   • Jaegug Bae

   Pages 31-37

5. The Brun-Titchmarsh Theorem on average

   • R. C. Baker, G. Harman

   Pages 39-103

6. Congruences for Fourier coefficients of half-integral weight modular forms and special values of L-functions

   • Antal Balog, Henri Darmon, Ken Ono

   Pages 105-128

7. The asymptotic formula for the number of representations of an integer as a sum of five squares

   • Paul T. Bateman

   Pages 129-139

8. Distribution of the error term for the number of lattice points inside a shifted ball

   • P. Bleher, J. Bourgain

   Pages 141-153

9. A probabilistic generalization of the Riemann zeta function

   • Nigel Boston

   Pages 155-162

10. A general Heine transformation and symmetric polynomials of Rogers

    • Douglas Bowman

    Pages 163-171

11. A Sieve Auxiliary Function

    • David Bradley

    Pages 173-210

12. Bounds on complete exponential sums

    • Todd Cochrane

    Pages 211-224

13. A note on the fourth power moment of the Riemann zeta-function

    • J. B. Conrey

    Pages 225-230

14. Effective estimates of exponential sums over primes

    • Hédi Daboussi

    Pages 231-244

15. On Products of Multiplicative Functions of Absolute Value at Most 1 Which are Composed with Linear Functions

    • Hubert Delange

    Pages 245-263

16. Combinatorial sieves of dimension exceeding one II

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

    Pages 265-308

17. Congruences for partition functions

    • Dennis Eichhorn, Ken Ono

    Pages 309-321

18. Fractional power large sieves

    • P. D. T. A. Elliott

    Pages 323-332

19. Some problems I presented or planned to present in my short talk

    • Paul Erdös

    Pages 333-335

20. On the number of divisors of n!

    • Paul Erdös, S. W. Graham, Aleksandar Ivić, Carl Pomerance

    Pages 337-355

On May 16 -20, 1995, approximately 150 mathematicians gathered at the Conference Center of the University of Illinois at Allerton Park for an Inter­ national Conference on Analytic Number Theory. The meeting marked the approaching official retirement of Heini Halberstam from the mathematics fac­ ulty of the University of Illinois at Urbana-Champaign. Professor Halberstam has been at the University since 1980, for 8 years as head of the Department of Mathematics, and has been a leading researcher and teacher in number theory for over forty years. The program included invited one hour lectures by G. Andrews, J. Bour­ gain, J. M. Deshouillers, H. Halberstam, D. R. Heath-Brown, H. Iwaniec, H. L. Montgomery, R. Murty, C. Pomerance, and R. C. Vaughan, and almost one hundred other talks of varying lengths. These volumes comprise contributions from most of the principal speakers and from many of the other participants, as well as some papers from mathematicians who were unable to attend. The contents span a broad range of themes from contemporary number theory, with the majority having an analytic flavor.

• Modular form
• Riemann zeta function
• analytic number theory
• distribution
• integral
• number theory
• zeta function

• Department of Mathematics, University of Illinois, Urbana, USA

  Bruce C. Berndt, Harold G. Diamond, Adolf J. Hildebrand

Policies and ethics