Math Honours: Multiple Zeta Values

نویسندگان

  • JONATHAN M. BORWEIN
  • WADIM ZUDILIN
چکیده

[1] EZ-Face [2] Michael Hoffman’s site contains some basic information about the MZVs. Hoffman also has a comprehensive list of references on MZVs and related stuff [3] Jonathan M. Borwein, David M. Bradley, David J. Broadhurst, and Petr Lisonek, “Special values of multidimensional polylogarithms,” Trans. Amer. Math. Soc. 353 (2001), 907–941 [4] Wadim Zudilin, “Algebraic relations for multiple zeta values,” Russian Math. Surveys 58:1 (2003), 1–29 [5] Jonathan M. Borwein and David M. Bradley, “Thirty Two Goldbach Variations,” Int. J. Number Theory 2:1 (2006), 65–103 [6] David M. Bradley, “Multiple q-Zeta Values,” Journal of Algebra 283:2 (2005), 752–798

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

Double Shuffle Relations of Euler Sums

Abstract. In this paper we shall develop a theory of (extended) double shuffle relations of Euler sums which generalizes that of multiple zeta values (see Ihara, Kaneko and Zagier, Derivation and double shuffle relations for multiple zeta values. Compos. Math. 142 (2)(2006), 307–338). After setting up the general framework we provide some numerical evidence for our two main conjectures. At the ...

متن کامل

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

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].

متن کامل

Evaluation of zeta function of the simplest cubic field at negative odd integers

In this paper, we are interested in the evaluation of the zeta function of the simplest cubic field. We first introduce Siegel’s formula for values of the zeta function of a totally real number field at negative odd integers. Next, we will develop a method of computing the sum of a divisor function for ideals, and will give a full description for a Siegel lattice of the simplest cubic field. Us...

متن کامل

A q-analog of Euler's decomposition formula for the double zeta function

The double zeta function was first studied by Euler in response to a letter from Goldbach in 1742. One of Euler’s results for this function is a decomposition formula, which expresses the product of two values of the Riemann zeta function as a finite sum of double zeta values involving binomial coefficients. Here, we establish a q-analog of Euler’s decomposition formula. More specifically, we s...

متن کامل

Double shuffle relations of double zeta values and the double Eisenstein series at level N

In their seminal paper, Gangl, Kaneko and Zagier defined a double Eisenstein series and used it to study the relations between double zeta values. One of their key ideas is to study the formal double space and apply the double shuffle relations. They also proved the double shuffle relations for the double Eisenstein series. More recently, Kaneko and Tasaka extended the double Eisenstein series ...

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:

دوره   شماره 

صفحات  -

تاریخ انتشار 2011