Computation and structure of character polylogarithms with applications to character Mordell-Tornheim-Witten sums

نویسندگان

  • David H. Bailey
  • Jonathan M. Borwein
چکیده

This paper extends tools developed in [10, 8] to study character polylogarithms. These objects are used to compute Mordell-Tornheim-Witten character sums and to explore their connections with multiple-zeta values (MZVs) and with their character analogues [17].

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Computation and theory of extended Mordell-Tornheim-Witten sums

We consider some fundamental generalized Mordell–Tornheim–Witten (MTW) zeta-function values along with their derivatives, and explore connections with multiplezeta values (MZVs). To achieve this, we make use of symbolic integration, high precision numerical integration, and some interesting combinatorics and special-function theory. Our original motivation was to represent unresolved constructs...

متن کامل

Computation and experimental evaluation of Mordell–Tornheim–Witten sum derivatives

In previous work the present authors and others have studied Mordell-Tornheim-Witten sums and their connections with multiple-zeta values. In this note we describe the numerical computation of derivatives at zero of a specialization originating in a preprint by Romik, and the experimental evaluation of these numerical values in terms of well-known constants.

متن کامل

Computation and theory of Mordell-Tornheim-Witten sums II

In [7] the current authors, along with the late and much-missed Richard Crandall (1947– 2012), considered generalized Mordell–Tornheim–Witten (MTW) zeta-function values along with their derivatives, and explored connections with multiple-zeta values (MZVs). This entailed use of symbolic integration, high precision numerical integration, and some interesting combinatorics and special-function th...

متن کامل

Reducibility of Signed Cyclic Sums of Mordell-tornheim Zeta and L-values

Matsumoto et al. define the Mordell-Tornheim L-functions of depth k by LMT(s1, . . . , sk+1;χ1, . . . , χk+1) := ∞ ∑

متن کامل

On Mordell-tornheim Sums and Multiple Zeta Values

RÉSUMÉ. Nous prouvons que toute somme de Mordell-Tornheim avec des arguments entiers positifs peut s’écrire comme une combinaison linéaire rationnelle de valeurs prises par des fonctions multi-zêta ayant le même poids et la même profondeur. Selon un résultat de Tsumura, il s’ensuit que toute somme de Mordell-Tornheim ayant un poids et une profondeur de parité différente peut s’exprimer comme un...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Math. Comput.

دوره 85  شماره 

صفحات  -

تاریخ انتشار 2016