Affiliation: Bringham Young University
Title Of Talk: Asymptotic formulas for positive definite quadratic forms
Abstract: Let Q be a positive definite integral quadratic form in 2 or more variables. Let r(Q,n) be the number of representations of n by Q (using integer vectors). One might expect to find in the literature an asymptotic formula for the sum of the squares of the r(Q,n) for n up to x, but this is not so, except for special cases. For example, it has been done for only finitely many binary forms. In this talk a general solution of the problem is given. An effort to put the constant multiplier in the asymptotic formula into closed form leads to a curious problem about quadratic forms over the ring of integers modulo 4.
Last update made Thu Mar 4 19:09:01 EST 2010.