Theta series of ternary quadratic forms

Abstract

We establish the linear independence of the theta series arising from the classes of even positive definite ternary forms of discriminant 2 p 2 which have a nontrivial automorphism group. p is assumed to be an odd prime number. We also consider even positive ternary forms over Z [(1 + √p)/2] of discriminant 2. In the case p ≡ 5 (mod 8), we show that those forms that represent 2 have independent generalized theta series.