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Class Number Divisibility in Real Quadratic Function Fields

Published online by Cambridge University Press:  20 November 2018

Christian Friesen
Christian Friesen*
Affiliation:
Mathematics Department University of Toronto Toronto, Ontario Canada
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Abstract

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Let q be a positive power of an odd prime p, and let Fq(t) be the function field with coefficients in the finite field of q elements. Let denote the ideal class number of the real quadratic function field obtained by adjoining the square root of an even-degree monic . The following theorem is proved: Let n ≧ 1 be an integer not divisible by p. Then there exist infinitely many monic, squarefree polynomials, such that n divides the class number, . The proof constructs an element of order n in the ideal class group.

Keywords

11A5511R29Continued FractionsFunction FieldsClass Numbers

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 3 , 01 September 1992, pp. 361 - 370
Copyright
Copyright © Canadian Mathematical Society 1992

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