Abstract
The celebrated Riemann–Siegel formula compares the Riemann zeta function on the critical line with its partial sums, expressing the difference between them as an expansion in terms of decreasing powers of the imaginary variable t. Siegel anticipated that this formula could be generalized to include the Hardy–Littlewood approximate functional equation, valid in any vertical strip. We give this generalization for the first time. The asymptotics contain Mordell integrals and an interesting new family of polynomials.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
