We show that if the Riemann Hypothesis is true for the Riemann zeta-function, ζ(s), and 0<a<1/2, then all but a finite number of the zeros of ℜζ(a+it), ℑζ(a+it), and similar functions are simple. We also study the pair correlation of the zeros of these functions assuming the Riemann Hypothesis is true and 0<a≤1/2.
Bibliographical noteFunding Information:
Research of the first author was partially supported by National Science Foundation grant DMS 1200582 . The first author also thanks Yonsei University and the Korea Institute for Advanced Study for their generous support and hospitality. Research of the second author was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (No. 2017R1A2B2002702 ).
© 2017 Elsevier Inc.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory