Number of the representations of integers by certain ternary quadratic forms

Abstract

Exact formulas are derived for the number of the representations of positive integers by certain positive ternary quadratic forms, belonging to multiclass genera. The Fourier coefficients of the corresponding cusp forms (on the basis of the known results of Waldspurger and Tunnell) are expressed in terms of the values of the Hasse-Weil L-functions of certain elliptic curves at the center of the critical strip.