Non-vanishing theta values of characters with special prime conductors.

Let p be a prime of the form 2 ℓ + 1 or 4 ℓ + 1 , where ℓ is also a prime. We prove θ (χ , i) ≠ 0 for all primitive Dirichlet characters χ with conductor p except for the quadratic and the quartic ones. Our results generalize a theorem of Bengoechea, which asserts θ (χ , i) ≠ 0 for non-quadratic χ with "large" prime conductor p = 2 ℓ + 1 , where ℓ is also a prime. [ABSTRACT FROM AUTHOR]