JOURNAL ARTICLE

A Dirichlet series related to the error term in the Prime Number Theorem.

  • Published In: International Journal of Number Theory, 2024, v. 20, n. 3. P. 715 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Elma, Ertan 3 of 3

Abstract

For a natural number n , let Z 1 (n) : = ∑ ρ n ρ ρ where the sum runs over the nontrivial zeros of the Riemann zeta function. For a primitive Dirichlet character χ modulo q ≥ 3 , we define Z 1 (s , χ) : = ∑ n = 1 ∞ χ (n) Z 1 (n) n s for ℜ (s) > 2 and obtain the meromorphic continuation of the function Z 1 (s , χ) to the region ℜ (s) > 1 2 . Our main result indicates that the poles of Z 1 (s , χ) in the region 1 2 < ℜ (s) < 1 , if they exist, are related to the zeros of many Dirichlet L -functions in the same region. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:International Journal of Number Theory. 2024/04, Vol. 20, Issue 3, p715
  • Document Type:Article
  • Subject Area:Science
  • Publication Date:2024
  • ISSN:1793-0421
  • DOI:10.1142/S1793042124500362
  • Accession Number:176852201
  • Copyright Statement:Copyright of International Journal of Number Theory is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Looking to go deeper into this topic? Look for more articles on EBSCOhost.