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Normalization of the Hyperadelic Gamma Function

  • Greg W. Anderson
Conference paper
Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 16)

Abstract

(0.1) Our goal is to solve a problem posed in the paper [A2]. Our goal in the introduction is to explain the problem, referring to [A1] and [A2] for details and background, but not supposing much familiarity with those papers. To get started, consider the functional equations

$$\begin{array}{l} B\left( {s,t} \right) = \Gamma \left( s \right)\Gamma \left( t \right)/\Gamma \left( {s + t} \right),\,B\left( {s,t} \right) = B\left( {t,s} \right),\\ B\left( {r,s} \right)B\left( {r + s,t} \right) = B\left( {r,s + t} \right)B\left( {s,t} \right) \end{array}$$
obeyed by the gamma and beta integrals
$$\Gamma (s)\, = \,\int_0^\infty {{e^{ - x}}{x^{s - 1}}\,dx,\,B(s,t)\, = \,\int_0^1 {{x^{s - 1}}} } {(1 - x)^{t - 1}}\,dx.$$

Keywords

Exact Sequence Prime Number Cohomology Class Closed Subgroup Inverse Limit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [A1]
    G. Anderson, Torsion points on Fermat Jacobians, roots of circular units and relative singular homology, Duke Math. J. 54 (1987), 501–561.MathSciNetCrossRefGoogle Scholar
  2. [A2]
    G. Anderson, The hyperadelic gamma function, Inv. Math., in press.Google Scholar
  3. [AT]
    E. Artin and J. Tate, “Class Field Theory,” W. A. Benjamin, Reading, Massachusetts, 1967.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1989

Authors and Affiliations

  • Greg W. Anderson
    • 1
  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA

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