Applications of a continued fraction algorithm to some class number problems

Author:
M. D. Hendy

Journal:
Math. Comp. **28** (1974), 267-277

MSC:
Primary 12A50; Secondary 10F20, 12A25

MathSciNet review:
0330102

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Abstract | References | Similar Articles | Additional Information

Abstract: We make extensive use of Lagrange's algorithm for the evaluation of the quotients in the continued fraction expansion of the quadratic surd , where for and for . The recursively generated terms in his algorithm lead to all norms of primitive algebraic integers of less than , *D* being the discriminant. By ensuring that the values contain at most one small prime, we are able to generate sequences of determinants *d* of real quadratic fields whose genera usually contain more than one ideal class. Formulae for their fundamental units are given.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0025-5718-1974-0330102-2

Keywords:
Principal ideals,
real quadratic field,
fundamental unit,
infinite continued fraction,
Lagrange algorithm,
class number,
genera,
Shanks sequence

Article copyright:
© Copyright 1974
American Mathematical Society