Shrinking the period lengths of continued fractions while still capturing convergents

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• 作者：Edward B. Burger ; Jesse Gell-Redman ; Ross Kravitz ; Daniel Walton ; Nicholas Yates
• 关键词：Shimura correspondence ; Half integral weight forms ; Special values of L-functions
• 刊名：Journal of Number Theory
• 出版年：2008
• 出版时间：January 2008
• 年：2008
• 卷：128
• 期：1
• 页码：144-153
• 全文大小：125 K

文摘

Here we prove that every real quadratic irrational α can be expressed as a periodic non-simple continued fraction having period length one. Moreover, we show that the sequence of rational numbers generated by successive truncations of this expansion is a sequence of convergents of α. We close with an application relating the structure of a quadratic α to its conjugate.