Zeta-functions of harmonic theta-series and prime numbers

The problem of separation of prime numbers presentable as values of quadratic polynomials, for example, of primes having the form $n^2+1$, naturally leads to the  question on Euler product factorization of zeta-functions corresponding to theta-series with harmonic coefficients. Two approaches to this question will be touched in the talk: one is based on the action of Hecke operators on harmonic theta-series and another is linked with interpretation of the zeta-functions, at least for certain binary quadratic forms, as L-functions of suitable quadratic rings with Hecke "Grossen" characters.