Zeros of $L$-functions attached to cusp forms of half-integral weight
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- by Jaban Meher, Sudhir Pujahari and Karam Deo Shankhadhar PDF
- Proc. Amer. Math. Soc. 147 (2019), 131-143 Request permission
Abstract:
In this paper, we study the zeros of $L$-functions attached to cusp forms of half-integral weight. Firstly, we find an explicit vertical strip in the complex plane in which all the non-trivial zeros of the $L$-function attached to a cusp form of half-integral weight lie. Secondly, we prove that the $L$-function attached to certain cusp forms of half-integral weight have infinitely many zeros of odd order on the critical line.References
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Additional Information
- Jaban Meher
- Affiliation: School of Mathematical Sciences, National Institute of Science Education and Research, Bhubaneswar, HBNI, P. O. Jatni, Khurda 752050, Odisha, India
- MR Author ID: 933713
- Email: jaban@niser.ac.in
- Sudhir Pujahari
- Affiliation: The University of Hong Kong, Pokfulam, Hong Kong
- MR Author ID: 1101430
- Email: sudhir@hku.hk
- Karam Deo Shankhadhar
- Affiliation: Department of Mathematics, Indian Institute of Science Education and Research Bhopal, Bhopal Bypass Road, Bhauri, Bhopal 462 066, Madhya Pradesh, India
- MR Author ID: 1021913
- Email: karamdeo@iiserb.ac.in
- Received by editor(s): May 3, 2018
- Received by editor(s) in revised form: May 17, 2018
- Published electronically: October 18, 2018
- Additional Notes: Karam Deo Shankhadhar served as corresponding author for this manuscript
The second author thanks Harish-Chandra Research Institute, Allahabad, where he was a postdoctoral fellow while working on this paper.
The research of the first and third authors was partially supported by the DST-SERB grants MTR/2017/000022 and ECR/2016/001359 respectively. - Communicated by: Amanda Folsom
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 131-143
- MSC (2010): Primary 11F37, 11F66, 11M41
- DOI: https://doi.org/10.1090/proc/14241
- MathSciNet review: 3876737