Published In

Mathematische Zeitschrift

Document Type

Pre-Print

Publication Date

7-13-2022

Subjects

Eigenvalues, Field Theory and Polynomials

Abstract

In this paper we estimate sums of the form ∑n≤X|aSymmπ(|f(n)|)|, for symmetric power lifts of automorphic representations π attached to holomorphic forms and polynomials f(x)∈Z[x] of arbitrary degree. We give new upper bounds for these sums under certain natural assumptions on f. Our results are unconditional when deg(f)≤4. Moreover, we study the analogous sum over polynomials in several variables. We obtain an estimate for all cubic polynomials in two variables that define elliptic curves.

Description

This is the author’s version of a work. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Mathematische Zeitschrift, 1-20.

DOI

10.1007/s00209-022-03071-y

Persistent Identifier

https://archives.pdx.edu/ds/psu/38375

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