SUM OF VALUES OF THE IDEAL CLASS ZETA-FUNCTION OVER NONTRIVIAL ZEROS OF THE RIEMANN ZETA-FUNCTION

We prove an upper bound for the sum of values of the ideal class zeta-function over nontrivial zeros of the Riemann zeta-function. The same result for the Dedekind zeta-function is also obtained. This may shed light on some unproved cases of the general Dedekind conjecture.

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Bibliographic Details
Published in:Bulletin of the Australian Mathematical Society 2024-04, Vol.109 (2), p.288-300
Main Authors: WANANIYAKUL, SAEREE, STEUDING, JÖRN, RUNGTANAPIROM, NITHI
Format: Article
Language:English
Subjects:
Upper bounds
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Description
Summary:We prove an upper bound for the sum of values of the ideal class zeta-function over nontrivial zeros of the Riemann zeta-function. The same result for the Dedekind zeta-function is also obtained. This may shed light on some unproved cases of the general Dedekind conjecture.
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972723000734