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arXiv · 1912.02909

Newton Polygons of Hecke Operators

Liubomir Chiriac·Andrei Jorza
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Abstract

In this computational paper we verify a truncated version of the Buzzard-Calegari conjecture on the Newton polygon of the Hecke operator $T_2$ 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 $n\leq 15$, then it agrees with the Newton polygon of $T_2$ up to $n$.

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Liubomir Chiriac, Andrei Jorza. 2019-12-05. Newton Polygons of Hecke Operators. https://doi.org/10.1007/s40316-020-00149-z

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