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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Zeros of derivatives of $L$-functions in the Selberg class on $\Re (s)<1/2$
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by Sneha Chaubey, Suraj Singh Khurana and Ade Irma Suriajaya
Proc. Amer. Math. Soc. 151 (2023), 1855-1866
DOI: https://doi.org/10.1090/proc/16251
Published electronically: February 17, 2023

Abstract:

In this article, we show that the Riemann hypothesis for an $L$-function $F$ belonging to the Selberg class implies that all the derivatives of $F$ can have at most finitely many zeros on the left of the critical line with imaginary part greater than a certain constant. This was shown for the Riemann zeta function by Levinson and Montgomery in 1974 [Acta Math. 133 (1974), pp. 49–65].
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Bibliographic Information
  • Sneha Chaubey
  • Affiliation: Department of Mathematics, Indraprastha Institute of Information Technology Delhi, New Delhi - 110020, India
  • MR Author ID: 1081961
  • Email: sneha@iiitd.ac.in
  • Suraj Singh Khurana
  • Affiliation: Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Uttar Pradesh – 208016, India
  • MR Author ID: 1325741
  • Email: suraj.singh.khurana@gmail.com
  • Ade Irma Suriajaya
  • Affiliation: Faculty of Mathematics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
  • MR Author ID: 1127084
  • ORCID: 0000-0003-3386-0990
  • Email: adeirmasuriajaya@math.kyushu-u.ac.jp
  • Received by editor(s): February 28, 2022
  • Received by editor(s) in revised form: July 24, 2022, and August 21, 2022
  • Published electronically: February 17, 2023
  • Additional Notes: Research of the first author was supported by the Science and Engineering Research Board, Department of Science and Technology, Government of India under grant SB/S2/RJN-053/2018. The second author was supported by National Board for Higher Mathematics (NBHM), Department of Atomic Energy (DAE), Government of India (DAE Ref no: 0204/37/2021/R&D-II/15564). Research of the third author was supported by JSPS KAKENHI Grant Number 18K13400 and MEXT Initiative for Realizing Diversity in the Research Environment.
  • Communicated by: Amanda Folsom
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 1855-1866
  • MSC (2020): Primary 11M41
  • DOI: https://doi.org/10.1090/proc/16251
  • MathSciNet review: 4556183