Under Artin's conjecture, an explicit asymptotic counts zeros of Artin L-functions up to height T, giving unconditional formulas for Hecke L-functions.
Estimating the number of zeros of Dedekind zeta-functions
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abstract
In this article, I derive a new approach to estimate the number of non-trivial zeros of a given Dedekind zeta function with absolute height at most $T\geq1$ counted with multiplicity. The error term in corresponding asymptotic formula improves all previous results, even in the case of the Riemann zeta function.
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2026 1verdicts
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Counting zeros of Artin $L$-functions
Under Artin's conjecture, an explicit asymptotic counts zeros of Artin L-functions up to height T, giving unconditional formulas for Hecke L-functions.