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1995 An investigation of bounds for the regulator of quadratic fields
Michael J. Jacobson, Jr., Richard F. Lukes, Hugh C. Williams
Experiment. Math. 4(3): 211-225 (1995).


It is well known that the nontorsion part of the unit group of a real quadratic field $\K$ is cyclic. With no loss of generality we may assume that it has a generator $\eps_{0} > 1$, called the fundamental unit of $\K$. The natural logarithm of $\eps_{0}$ is called the regulator R of $\K$. This paper considers the following problems: How large, and how small, can R get? And how often?

The answer is simple for the problem of how small R can be, but seems to be extremely difficult for the question of how large R can get. In order to investigate this, we conducted several large-scale numerical experiments, involving the Extended Riemann Hypothesis and the Cohen--Lenstra class number heuristics. These experiments provide numerical confirmation for what is currently believed about the magnitude of R.


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Michael J. Jacobson, Jr.. Richard F. Lukes. Hugh C. Williams. "An investigation of bounds for the regulator of quadratic fields." Experiment. Math. 4 (3) 211 - 225, 1995.


Published: 1995
First available in Project Euclid: 3 September 2003

zbMATH: 0859.11057
MathSciNet: MR1387478

Primary: 11R42
Secondary: 11R11 , 11R29 , 11Y40

Rights: Copyright © 1995 A K Peters, Ltd.

Vol.4 • No. 3 • 1995
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