University of Illinois at Urbana-Champaign
Department of Mathematics
Colloquium
by
Prof. Trevor Wooley

4:00 PM, Thursday, December 4, 1997, 245 Altgeld Hall.

On Exponential Sums, and the Solubility of Diophantine Equations in Many Variables
A problem of interest in analytic number theory (as an application of the Hardy-Littlewood method), as well as in arithmetic geometry, concerns the asymptotic formula for the number of integral points inside a large box satisfying a system of homogeneous diophantine equations. In this talk we will discuss what is known (not much in general!). We will also develop some exponential sum estimates of use in such problems, and mention some applications.

Additional References:

  1. W. M. Schmidt, Analytic methods for congruences, Diophantine equations and approximations, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warszaw, 1983), PWN, Warszaw, 1984, pp. 515-524.
  2. D. J. Lewis, Diophantine problems: solved and unsolved, in Number theory and applications, ed. R. A. Mollin, Kluwer Academic Publishers, 1989, pp. 103-121.