Newton Polygons of Hecke Operators

Authors

Liubomir Chiriac, Portland State UniversityFollow
Andrei Jorza, University of Notre Dame

Published In

Annales Mathematiques Du Quebec

Document Type

Post-Print

Publication Date

10-13-2020

Abstract

In this computational paper we verify a truncated version of the Buzzard–Calegari conjecture on the Newton polygon of the Hecke operator T2 for all large enough weights. We first develop a formula for computing p-adic valuations of exponential sums, which we then implement to compute 2-adic valuations of traces of Hecke operators acting on spaces of cusp forms. Finally, we verify that if Newton polygon of the Buzzard–Calegari polynomial has a vertex at n≤15, then it agrees with the Newton polygon of T2 up to n.

Rights

This is a post-print originally published by Springer Nature, in Annales Mathematiques Du Quebec, October 2020. You can find the original version: https://doi.org/10.1007/s40316-020-00149-z

Locate the Document

https://doi.org/10.1007/s40316-020-00149-z

DOI

10.1007/s40316-020-00149-z

Persistent Identifier

https://archives.pdx.edu/ds/psu/34434

Citation Details

Chiriac, L., & Jorza, A. (2020). Newton polygons of Hecke operators. Annales Mathématiques Du Québec. https://doi.org/10.1007/s40316-020-00149-z