Special Values of Zeta Functions Associated with Self-Dual Homogeneous Cones

  • I. Satake
Part of the Progress in Mathematics book series (PM, volume 14)


To explain the main idea of this paper, and also to fix some notations, we start with reviewing the classical case of Riemann zeta function. As usual we set
$$\varsigma \left( s \right) = \sum\limits_{n = 1}^\infty {{n^{ - s}}} \quad \left( {Re\,s >1} \right)$$
$$\Gamma \left( s \right) = \int\limits_0^\infty {{x^{s - 1}}{e^{ - x}}dx\quad \left( {{\mathop{\rm Re}\nolimits} \,s >0} \right)}$$


Zeta Function Haar Measure Jordan Algebra Maximal Compact Subgroup Laurent Expansion 
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Copyright information

© Springer Science+Business Media New York 1981

Authors and Affiliations

  • I. Satake
    • 1
    • 2
  1. 1.University of CaliforniaBerkeleyUSA
  2. 2.Tôhoku UniversitySendai 980Japan

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