Summing Hecke eigenvalues over polynomials

Liubomir Chiriac, Liyang Yang

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)643-662
Number of pages20
JournalMathematische Zeitschrift
Volume302
Issue number2
DOIs
StatePublished - Oct 2022

All Science Journal Classification (ASJC) codes

  • General Mathematics

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