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On the Size of the Wild Set

  Published:2005-02-01
 Printed: Feb 2005
  • Marius Somodi
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Abstract

To every pair of algebraic number fields with isomorphic Witt rings one can associate a number, called the {\it minimum number of wild primes}. Earlier investigations have established lower bounds for this number. In this paper an analysis is presented that expresses the minimum number of wild primes in terms of the number of wild dyadic primes. This formula not only gives immediate upper bounds, but can be considered to be an exact formula for the minimum number of wild primes.
MSC Classifications: 11E12, 11E81, 19F15, 11R29 show english descriptions Quadratic forms over global rings and fields
Algebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24]
Symbols and arithmetic [See also 11R37]
Class numbers, class groups, discriminants
11E12 - Quadratic forms over global rings and fields
11E81 - Algebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24]
19F15 - Symbols and arithmetic [See also 11R37]
11R29 - Class numbers, class groups, discriminants
 

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