A generalization of the riemann zeta-function

  • K. Ramachandra
  • I. V. Volovich


A generalization of the Riemann zeta-function which has the form
$$\zeta _\alpha (s) = \prod\limits_p {\frac{1}{{1 - p^{ - s} + (p + a)^{ - 3} }}} $$
is considered. Analytical properties with respect to s and asymptotic behaviour whena → ∞ are investigated. The correspondingL-function is also discussed. This consideration has an application in the theory ofp-adic strings.


Riemann zeta-function 


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  1. [1]
    Titchmarsh E C,The theory of the Riemann zeta-function, (Oxford: Clarendon Press) (1986)zbMATHGoogle Scholar
  2. [2]
    Areféva I Ya, Dragovič B, Volovich I V,On the Adelic string Amplitudes, Preprint, Institute of Physics, Beograd (1988)Google Scholar

Copyright information

© Indian Academy of Sciences 1989

Authors and Affiliations

  • K. Ramachandra
    • 1
  • I. V. Volovich
    • 1
    • 2
  1. 1.Tata Institute of Fundamental ResearchBombayIndia
  2. 2.Steklov Mathematical InstituteMoscowUSSR

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