UNFOLDING THE DOUBLE SHUFFLE STRUCTURE OF -MULTIPLE ZETA VALUES
نویسندگان
چکیده
منابع مشابه
Shuffle Product Formulas of Multiple Zeta Values
Using the combinatorial description of shuffle product, we prove or reformulate several shuffle product formulas of multiple zeta values, including a general formula of the shuffle product of two multiple zeta values, some restricted shuffle product formulas of the product of two multiple zeta values, and a restricted shuffle product formula of the product of n multiple zeta values.
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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 ...
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We study the higher order shuffle regularization for multiple zeta values and define higher order regularized shuffle relations. We find that higher order regularized shuffle relations can be deduced from the group-like property of the Drinfel’d associator.
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In this short note we will provide a new proof of the following exotic shuffle relation of multiple zeta values: ζ({2}x{3, 1}) = ( 2n+m m ) π (2n+ 1) · (4n+ 2m+ 1)! . This was proved by Zagier when n = 0, by Broadhurst when m = 0, and by Borwein, Bradley, and Broadhurst when m = 1. In general this was proved by Bowman and Bradley. Our new idea is to use the method of Borwein et al. to reduce th...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2015
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972715000167