Singular series of genus 2 for sums of squares

Abstract

Let f1, ..., fh be representatives of classes in the genus of a positive quadratic form f, ri(k) the number of representations of k by the form fi, ρ(k) the value of the singular Hardy-Littlewood series, Ei the number of integer automorphisms of fi. We derive an expression for in terms of the values of singular series of genus 1 and 2. This expression is evaluated for the simplest model f(x)=x 1 2 +...+x m 2 , m≡1 (mod 8), k is a prime in-integer, k=1(mod 8).

Locations

• Journal of Soviet Mathematics - View - PDF