| Title |
Zeros of the extended Selberg class zeta-functions and of their derivatives / |
| Authors |
Garunkštis, Ramūnas |
| DOI |
10.3906/mat-1904-36 |
| Full Text |
|
| Is Part of |
Turkish journal of mathematics.. Scientific and Technological Research Council of Turkey. 2019, Vol. 43, no. 6, p. 2921-2930.. ISSN 1300-0098 |
| Keywords [eng] |
Riemann zeta-function ; extended Selberg class ; nontrivial zeros ; Speiser's equivalent for the Riemann hypothesis |
| Abstract [eng] |
Levinson and Montgomery proved that the Riemann zeta-function zeta(s) and its derivative have approximately the same number of nonreal zeros left of the critical line. Spira showed that zeta'(1/2+it) = 0 implies that zeta(1/2+it) = 0. Here we obtain that in small areas located to the left of the critical line and near it the functions zeta(s) and zeta'(s) have the same number of zeros. We prove our result for more general zeta-functions from the extended Selberg class S. We also consider zero trajectories of a certain family of zeta-functions from S. |
| Published |
Scientific and Technological Research Council of Turkey |
| Type |
Journal article |
| Language |
English |
| Publication date |
2019 |
| CC license |
|
