| Upper Bounds of the Class Number and the Fundamental Unit of Real Quadratic Field ${\bf Q}(\sqrt{p})$ |
| Received:August 09, 2004 Revised:November 25, 2005 |
| Key Words:
real quadratic field class number fundamental unit upper bound prime.
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| Fund Project:the Science Foundation of the Education Department of Sichuan Province (2004B025) |
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| Abstract: |
| Let $p$ be an odd prime. Let $h$ and $\varepsilon$ denote the class number and the fundamental unit of the real quadratic field ${\bf Q}(\sqrt{p})$, respectively. This paper proves that if $p\equiv 1(\mod4)$, then $h\log\varepsilon<\frac{1}{4}(\sqrt{p}+6)\log(2e\sqrt{p})$. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2007.02.026 |
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