On von Staudt for Bernoulli-Carlitz numbers

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• 作者：José ; Alejandro Lara Rodrí ; guez^a ; ^b ; ^{lrodri@uady.mx} ; ^{jlara@ctrl.cinvestav.mx}
• 关键词：Function fields ; Drinfeld modules ; Denominators ; Bernoulli numbers
• 刊名：Journal of Number Theory
• 出版年：2012
• 出版时间：April 2012
• 年：2012
• 卷：132
• 期：4
• 页码：495-501
• 全文大小：140 K

文摘

In 1935, Carlitz introduced analogues of Bernoulli numbers for . These are now called Bernoulli-Carlitz numbers . He proved a von Staudt type theorem, with a much more subtle statement than the classical one, describing their denominators completely. As an analog of the important relative of the usual Bernoulli number , Thakur considered an analog , where is the Carlitz factorial. He described their denominator fully except when and m has a particular form. The purpose of this paper is to completely describe this last remaining situation. Also, we shall see that a group of symmetries recently discovered by Goss may be realized as symmetries of our results.