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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Counting zeros of Dedekind zeta functions
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by Elchin Hasanalizade, Quanli Shen and Peng-Jie Wong HTML | PDF
Math. Comp. 91 (2022), 277-293

Abstract:

Given a number field $K$ of degree $n_K$ and with absolute discriminant $d_K$, we obtain an explicit bound for the number $N_K(T)$ of non-trivial zeros (counted with multiplicity), with height at most $T$, of the Dedekind zeta function $\zeta _K(s)$ of $K$. More precisely, we show that for $T \geq 1$, \begin{equation*} \Big | N_K (T) - \frac {T}{\pi } \log \Big ( d_K \Big ( \frac {T}{2\pi e}\Big )^{n_K}\Big )\Big | \le 0.228 (\log d_K + n_K \log T) + 23.108 n_K + 4.520, \end{equation*} which improves previous results of Kadiri and Ng, and Trudgian. The improvement is based on ideas from the recent work of Bennett et al. on counting zeros of Dirichlet $L$-functions.
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Additional Information
  • Elchin Hasanalizade
  • Affiliation: Department of Mathematics and Computer Science, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta T1K 3M4, Canada
  • ORCID: 0000-0003-2604-7221
  • Email: e.hasanalizade@uleth.ca
  • Quanli Shen
  • Affiliation: Department of Mathematics and Computer Science, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta T1K 3M4, Canada
  • MR Author ID: 1166842
  • ORCID: 0000-0003-3095-3702
  • Email: quanli.shen@uleth.ca
  • Peng-Jie Wong
  • Affiliation: Department of Mathematics and Computer Science, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta T1K 3M4, Canada
  • MR Author ID: 1211484
  • Email: pengjie.wong@uleth.ca
  • Received by editor(s): July 18, 2020
  • Received by editor(s) in revised form: April 5, 2021
  • Published electronically: July 19, 2021
  • Additional Notes: The second and third authors are the corresponding authors. This research was supported by the NSERC Discovery grants RGPIN-2020-06731 of Habiba Kadiri and RGPIN-2020-06032 of Nathan Ng. The third author was supported by a PIMS postdoctoral fellowship and the University of Lethbridge
  • © Copyright 2021 Elchin Hasanalizade, Quanli Shen, and Peng-Jie Wong
  • Journal: Math. Comp. 91 (2022), 277-293
  • MSC (2020): Primary 11R42
  • DOI: https://doi.org/10.1090/mcom/3665
  • MathSciNet review: 4350540