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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Class numbers of totally imaginary quadratic extensions of totally real fields
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by Judith S. Sunley PDF
Trans. Amer. Math. Soc. 175 (1973), 209-232 Request permission

Abstract:

Let K be a totally real algebraic number field. This paper provides an effective constant $C(K,h)$ such that every totally imaginary quadratic extension L of K with ${h_L} = h$ satisfies $|{d_L}| < C(K,h)$ with at most one possible exception. This bound is obtained through the determination of a lower bound for $L(1,\chi )$ where $\chi$ is the ideal character of K associated to L. Results of Rademacher concerning estimation of L-functions near $s = 1$ are used to determine this lower bound. The techniques of Tatuzawa are used in the proof of the main theorem.
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 175 (1973), 209-232
  • MSC: Primary 12A50
  • DOI: https://doi.org/10.1090/S0002-9947-1973-0311622-9
  • MathSciNet review: 0311622