Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897106 | Journal of Number Theory | 2018 | 10 Pages |
Abstract
Occurrences of very close zeros of the Riemann zeta function are strongly connected with Lehmer pairs and with the Riemann Hypothesis. The aim of the present note is to derive a condition for a pair of consecutive simple zeros of the ζ-function to be a Lehmer pair in terms of derivatives of Hardy's Z-function. Furthermore, we connect Newman's conjecture with stationary points of the Z-function, and present some numerical results.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Aleksander SimoniÄ,