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Zeta-functions of A-fields

  • André Weil
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 144)

Abstract

From now on, k will be an A-field of any characteristic, either 0 or p> 1. Notations will be as before; if v is a place of k, k v is the completion of k at v; if v is a finite place, r v is the maximal compact subring of k v , and p v the maximal ideal in r v . Moreover, in the latter case, we will agree once for all to denote by q v the module of the field k v and by π v a prime element of k v , so that, by th. 6 of Chap. I–4, r v /p v is a field with q v elements, and |π v | v = q v - 1. If k is of characteristic p> 1, we will denote by q the number of elements of the field of constants of k and identify that field with F q ; then, according to the definitions in Chap. VI, we have q v = q deg (v ) for every place v.

Keywords

Meromorphic Function Haar Measure Standard Function Open Subgroup Finite 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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Copyright information

© Springer Science+Business Media New York 1973

Authors and Affiliations

  • André Weil
    • 1
  1. 1.The Institute for Advanced StudyPrincetonUSA

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