Abstract
Let p be a prime of the form 2ℓ+1 or 4ℓ+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=2ℓ+1, where ℓ is also a prime.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.