The p-adic L-function for half-integral weight modular forms

Mercuri, Salvatore

Abstract

The p-adic L-function for modular forms of integral weight is well-known. For certain weights the p-adic L-function for modular forms of half-integral weight is also known to exist, via a correspondence, established by Shimura, between them and forms of integral weight. However, we construct it here without any recourse to the Shimura correspondence, allowing us to establish its existence for all weights, including those exempt from the Shimura correspondence. We do this by employing the Rankin–Selberg method, and proving explicit p-adic congruences in the resultant Rankin–Selberg expression.

Citation

Mercuri, S. (2020). The p-adic L-function for half-integral weight modular forms. manuscripta mathematica, 161(1-2), 61-91. https://doi.org/10.1007/s00229-018-1085-1

• Journal Article Type: Article
• Acceptance Date: Oct 30, 2018
• Online Publication Date: Nov 7, 2018
• Publication Date: Jan 31, 2020
• Deposit Date: Nov 23, 2018
• Publicly Available Date: Nov 23, 2018
• Journal: manuscripta mathematica
• Print ISSN: 0025-2611
• Electronic ISSN: 1432-1785
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 161
• Issue: 1-2
• Pages: 61-91
• DOI: https://doi.org/10.1007/s00229-018-1085-1
• Related Public URLs: http://community.dur.ac.uk/salvatore.mercuri/padiclfun.pdf