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1999 Some methods for evaluating the regulator of a real quadratic function field
Andreas Stein, Hugh C. Williams
Experiment. Math. 8(2): 119-133 (1999).

Abstract

We develop methods for the rapid computation of the regulator of a real quadratic congruence function field $K=k(x)({\sqrt{D}})$. By extending Shanks' infrastructure ideas in real quadratic number fields to real quadratic congruence function fields we obtain a baby step-giant step method for evaluating the regulator of K in $O( |D|\supfrac 14 )$ polynomial operations. We also show the existence of an effective algorithm which computes the regulator unconditionally in $O( |D|\supfrac 15 )$ polynomial operations. By implementing both methods on a computer, we found that the $O( |D|\supfrac 15 )$-algorithm tends to be far better than the baby step-giant step algorithm in those cases where the regulator exceeds $10^8$.

Citation

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Andreas Stein. Hugh C. Williams. "Some methods for evaluating the regulator of a real quadratic function field." Experiment. Math. 8 (2) 119 - 133, 1999.

Information

Published: 1999
First available in Project Euclid: 12 March 2003

zbMATH: 0987.11071
MathSciNet: MR1700574

Subjects:
Primary: 11R58
Secondary: 11Y40 , 11Y65

Rights: Copyright © 1999 A K Peters, Ltd.

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Vol.8 • No. 2 • 1999
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