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
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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].References
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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