ZEROS OF THE PERIODIC HURWITZ ZETA-FUNCTION

Author:

Ram\={u}nas GARUNK\v{S}TIS, Rokas TAMO\v{S}I\={U}NAS

2010 Mathematics Subject Classification:

11M35, 11M41.

Keywords:

Hurwitz zeta-function, Lerch zeta-function, nontrivial zeros, periodic Hurwitz zeta-function.

Abstract:

We consider the zero distribution of the periodic Hurwitz zeta-function.  Among other results, we obtain an asymptotic formula for the number of nontrivial zeros up to a given height and show that zeros are clustered around the critical line. We also draw several pictures of real and imaginary lines of the Hurwitz zeta-function.

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Garu-Tamo-2013

Vol. 8 (16), 2013