JOURNAL ARTICLE

On irrationality criteria for the Ramanujan summation of certain series.

  • Published In: International Journal of Number Theory, 2023, v. 19, n. 7. P. 1571 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Khurana, Suraj Singh 3 of 3

Abstract

In this paper, we prove a criterion for the irrationality of certain constants which arise from the Ramanujan summation of a family of infinite divergent sums. As an application, we provide a sufficient criterion for the irrationality of the values of the Riemann zeta function in the interval (0 , 1). We further see that our discussion leads to a natural generalization of a result of Sondow on the irrationality criterion for the Euler–Mascheroni constant. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:International Journal of Number Theory. 2023/08, Vol. 19, Issue 7, p1571
  • Document Type:Article
  • Subject Area:History
  • Publication Date:2023
  • ISSN:1793-0421
  • DOI:10.1142/S179304212350077X
  • Accession Number:167306692
  • 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.)

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