Rapidly convergent series representations of symmetric Tornheim double zeta functions について (解析的整数論とその周辺)

この論説は、論文「Rapidlyconvergent series representations of symmetricTornheim double zeta functions [8]」を解説したものである．§1では2つのキーワード「desingularization」と「Rapidlyconvergent series representations」について説明でする．§2.1ではTornheim2重ゼータ関数について簡単にまとめ，§2.2で主結果について記述し，§2.3では幾つかの注意を述べる．証明はここでは詳しく述べないので，論文を参照していただきたい．昨年度講究録の訂正 [71

Hilbert's inequality and Witten's zeta-function

In this article we explore a variety of pleasing connections between analysis, number theory, and operator theory, while revisiting a number of beautiful inequalities originating with Hilbert, Hardy and others. We first establish the Hilbert inequality and then apply it to various multiple zeta values. In consequence we obtain the norm of the classical Hilbert matrix, in the process illustrating the interplay of numerical and symbolic computation with classical mathematics