𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Arithmetic progressions of zeros of the Riemann zeta function

✍ 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.

✦ 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.


πŸ“œ SIMILAR VOLUMES


Linear statistics for zeros of Riemann's
✍ Chris Hughes; ZeΓ©v Rudnick πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 60 KB

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.

Simple zeros and discrete moments of the
✍ RamΕ«nas Garunks˘tis; JΓΆrn Steuding πŸ“‚ Article πŸ“… 2005 πŸ› Elsevier Science 🌐 English βš– 165 KB

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.