A Chebotarev Variant of the Brun-Titchmarsh Theorem and Bounds for the Lang-Trotter conjectures

Jesse Thorner, Asif Zaman

Research output: Contribution to journalArticlepeer-review

Abstract

Weimprove the Chebotarev variant of the Brun-Titchmarsh theorem proven by Lagarias, Montgomery, and Odlyzko using the log-free zero density estimate and zero repulsion phenomenon for Hecke L-functions that were recently proved by the authors. Our result produces an improvement for the best unconditional bounds toward two conjectures of Lang and Trotter regarding the distribution of traces of Frobenius for elliptic curves and holomorphic cuspidal modular forms. We also obtain new results on the distribution of primes represented by positive-definite integral binary quadratic forms.

Original languageEnglish (US)
Pages (from-to)4991-5027
Number of pages37
JournalInternational Mathematics Research Notices
Volume2018
Issue number16
DOIs
StatePublished - Aug 21 2018
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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