Arithmetic progressions of zeros of the Riemann zeta function
β Scribed by Machiel van Frankenhuijsen
- Publisher
- Elsevier Science
- Year
- 2005
- Tongue
- English
- Weight
- 168 KB
- Volume
- 115
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
β¦ Synopsis
If the Riemann zeta function vanishes at each point of the finite arithmetic progression {D + inp} 0<|n| 0), then N < 13p if D = 1/2, and N < p 1/D-1+o(1) in general.
π SIMILAR VOLUMES
We consider a smooth counting function of the scaled zeros of the Riemann zeta function, around height T . We show that the first few moments tend to the Gaussian moments, with the exact number depending on the statistic considered.
We prove unconditional upper bounds for the second and fourth discrete moment of the first derivative of the zeta-function at its simple zeros on the critical line.