The p-adic analytic Dedekind sums

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• 作者：Su Hu^a ; ^{mahusu@scut.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Min-Soo Kim^b ; ^{mskim@kyungnam.ac.kr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：11F20 ; 11B68 ; 11S80 ; 11M35
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：171
• 期：Complete
• 页码：112-127
• 全文大小：336 K

文摘

In this paper, using Cohen's and Tangedal and Young's theory on the p-adic Hurwitz zeta functions, we construct the analytic Dedekind sums on the p  -adic complex plane C_p${\mathbb{C}}_p$. We show that these Dedekind sums interpolate Carlitz's higher order Dedekind sums p-adically. From Apostol's reciprocity law for the generalized Dedekind sums, we also prove a reciprocity relation for the special values of these p-adic Dedekind sums. Finally, the parallel results for the analytic Dedekind sums on the p-adic complex plane associated with Euler polynomials have also been given.