Congruences Involving Alternating Multiple Harmonic Sums
نویسنده
چکیده
We show that for any prime prime p = 2, p−1 k=1 (−1) k k − 1 2 k ≡ − (p−1)/2 k=1 1 k (mod p 3) by expressing the left-hand side as a combination of alternating multiple harmonic sums.
منابع مشابه
Congruences involving alternating multiple harmonic sum
We show that for any prime prime p = 2 p−1 k=1 (−1) k k − 1 2 k ≡ − (p−1)/2 k=1 1 k (mod p 3) by expressing the l.h.s. as a combination of alternating multiple harmonic sums.
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متن کاملStatement 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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By convention we set H(s;n) = 0 any n < d. We call l(s) := d and |s| := ∑d i=1 |si| its depth and weight, respectively. We point out that l(s) is sometimes called length in the literature. When every si is positive we recover the multiple harmonic sums (MHS for short) whose congruence properties are studied in [9, 10, 17, 18]. There is another “non-strict” version of the AMHS defined as follows...
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 17 شماره
صفحات -
تاریخ انتشار 2010