Multiple zeta values and Euler sums
نویسندگان
چکیده
منابع مشابه
Central Binomial Sums, Multiple Clausen Values, and Zeta Values
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 ra...
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0. In 1978, Apéry showed the irrationality of ζ(3) = ∑∞ n=1 1 n3 by giving the approximants `n = unζ(3) − vn ∈ Qζ(3) + Q, un, dnvn ∈ Z, dn = l.c.m.(1, 2, . . . , n), with the property |`n| → ( √ 2 − 1) < 1/e as n → ∞. A similar approach was put forward to show the irrationality of ζ(2) (which is π/6, hence transcendental thanks to Lindemann) but I will concentrate on the case of ζ(3). A few mon...
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. . . , s k are positive integers with s 1 > 1. For k ≤ n, let E(2n, k) be the sum of all multiple zeta values with even arguments whose weight is 2n and whose depth is k. The well-known result E(2n, 2) = 3ζ(2n)/4was extended to E(2n, 3) and E(2n, 4) by Z. Shen and T. Cai. Applying the theory of symmetric functions, Hoffman gave an explicit generating function for the numbers E(2n, k) and then ...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2017
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2017.01.018