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    • Dirichlet Expression for $L(1, \chi)$ with General Dirichlet Character

      V V Rane

      Volume 120 Issue 1 February 2010 pp 7-9

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/120/01/0007-0009

    • Keywords

       

      Hurwitz zeta function; Dirichlet character; Dirichlet 𝐿-series; primitive character.

    • Abstract

       

      In the famous work of Dirichlet on class number formula, $L(s, \chi)$ at $s=1$ has been expressed as a finite sum, where $L(s, \chi)$ is the Dirichlet 𝐿-series of a real Dirichlet character. We show that this expression with obvious modification is valid for the general primitive Dirichlet character 𝜒.

    • Author Affiliations

       

      V V Rane1

      1. Department of Mathematics, The Institute of Science, 15, Madam Cama Road, Mumbai 400 032, India

    • Dates

       
      Published
      February 2010
      Manuscript received
      13 April 2007

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