LINEAR COMBINATIONS OF HURWITZ ZETA-FUNCTIONS

LINEAR COMBINATIONS OF HURWITZ ZETA-FUNCTIONS

We study the distribution of zeros of finite linear combinations of Hurwitz zeta-functions plus an arbitrary constant, and prove a Riemann-von Mangoldt type formula for their number of non-trivial zeros. Finally, as an application, we show that two Hurwitz zeta-functions sharing a complex value are...

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Veröffentlicht in:Kyushu Journal of Mathematics 2022, Vol.76(1), pp.27-41
Hauptverfasser: STEUDING, Rasa, STEUDING, Jörn
Format: Artikel
Sprache:eng
Schlagworte:
Hurwitz zeta-function
sharing values
zero-distribution
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Zusammenfassung:We study the distribution of zeros of finite linear combinations of Hurwitz zeta-functions plus an arbitrary constant, and prove a Riemann-von Mangoldt type formula for their number of non-trivial zeros. Finally, as an application, we show that two Hurwitz zeta-functions sharing a complex value are already identical, as well as a similar (more general) result about the uniqueness of linear combinations.
ISSN:1340-6116
1883-2032
DOI:10.2206/kyushujm.76.27