Central Binomial Sums, Multiple Clausen Values, and Zeta Values
نویسندگان
چکیده
We find and prove relationships between Riemann zeta values and central binomial sums. We also investigate alternating binomial sums (also called Apéry sums). The study of non-alternating sums leads to an investigation of different types of sums which we call multiple Clausen values. The study of alternating sums leads to a tower of experimental results involving polylogarithms in the golden ratio. In the non-alternating case, there is a strong connection to polylogarithms of the sixth root of unity, encountered in the 3-loop Feynman diagrams of hep-th/9803091 and subsequently in hep-ph/9910223, hep-ph/9910224, cond-mat/9911452 and hep-th/0004010. AMS (1991) subject classification: Primary 40B05, 33E20, Secondary 11M99, 11Y99.
منابع مشابه
Statement Julian
My mathematical research interests are in number theory and algebraic geometry. My thesis work concerns the arithmetic of a family of rational numbers known as multiple harmonic sums, which are truncated approximations of multiple zeta values. I explore new structures underlying relations involving multiple harmonic sums, p-adic L-values, Bernoulli numbers, and binomial coefficients. This is us...
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عنوان ژورنال:
- Experimental Mathematics
دوره 10 شماره
صفحات -
تاریخ انتشار 2001