| Автор | Jacobson, Michael J. |
| Автор | Lukes, Richard F. |
| Автор | Williams, Hugh C. |
| Дата выпуска | 1995 |
| dc.description | 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 ∊<sub>0</sub> > 1, called the fundamental unit of K. The natural logarithm of ∊<sub>0</sub> 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-scalenumerical experiments, involving the ExtendedRiemann Hypothesis and the Cohen-Lenstra class number heuristics. These experiments provide numerical confirmation for what is currently believed about the magnitude of R. |
| Формат | application.pdf |
| Издатель | Taylor & Francis Group |
| Копирайт | Copyright Taylor and Francis Group, LLC |
| Название | An Investigation of Bounds for the Regulator of Quadratic Fields |
| Тип | research-article |
| DOI | 10.1080/10586458.1995.10504322 |
| Electronic ISSN | 1944-950X |
| Print ISSN | 1058-6458 |
| Журнал | Experimental Mathematics |
| Том | 4 |
| Первая страница | 211 |
| Последняя страница | 225 |
| Аффилиация | Jacobson, Michael J.; Department of Computer Science, University of Manitoba |
| Аффилиация | Lukes, Richard F.; Department of Computer Science, University of Manitoba |
| Аффилиация | Williams, Hugh C.; Department of Computer Science, University of Manitoba |
| Выпуск | 3 |
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