Normalization of the Hyperadelic Gamma Function

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


(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
$$\Gamma (s)\, = \,\int_0^\infty {{e^{ - x}}{x^{s - 1}}\,dx,\,B(s,t)\, = \,\int_0^1 {{x^{s - 1}}} } {(1 - x)^{t - 1}}\,dx.$$


Exact Sequence Prime Number Cohomology Class Closed Subgroup Inverse Limit 
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  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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