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Bounded gaps between primes in Chebotarev sets

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Last modified
  • 02/20/2025
Type of Material
Authors
    Jesse Thorner, Emory University
Language
  • English
Date
  • 2014
Publisher
  • SpringerOpen
Publication Version
Copyright Statement
  • © 2014 Thorner; licensee Springer.
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Final Published Version (URL)
Title of Journal or Parent Work
Volume
  • 1
Issue
  • 4
Grant/Funding Information
  • This article was partially funded from Emory University's Open Access Publishing Fund.
Abstract
  • p1-p2
  •  ≤ 600 as a consequence of the Bombieri-Vinogradov Theorem. In this paper, we apply his general method to the setting of Chebotarev sets of primes. Methods: We use recent developments in sieve theory due to Maynard and Tao in conjunction with standard results in algebraic number theory. Results: Given a Galois extension, we prove the existence of bounded gaps between primes p having the same Artin symbol. Conclusions: We study applications of these bounded gaps with an emphasis on ranks of prime quadratic twists of elliptic curves over congruence properties of the Fourier coefficients of normalized Hecke eigenforms, and representations of primes by binary quadratic forms.
  • Purpose: A new and exciting breakthrough due to Maynard establishes that there exist infinitely many pairs of distinct primes p1, p2 with
Author Notes
  • Correspondence: Jesse Thorner, Department of Mathematics and Computer Science, Emory University, 400 Dowman Drive, Atlanta 30322, Georgia, USA. Email: jesse.thorner@emory.edu.
Keywords
Research Categories
  • Mathematics
  • Computer Science

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