Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4594217 | Journal of Number Theory | 2013 | 27 Pages |
Abstract
TextWe prove congruences, modulo a power of a prime p , for certain finite sums involving central binomial coefficients (2kk), partly motivated by analogies with the well-known power series for (arcsinz)2 and (arcsinz)4. The right-hand sides of those congruences involve values of the finite polylogarithms £d(x)=∑k=1p−1xk/kd. Exploiting the available functional equations for the latter we compute those values, modulo the required powers of p, in terms of familiar quantities such as Fermat quotients and Bernoulli numbers.VideoFor a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=W54Ad0YFr8A.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Sandro Mattarei, Roberto Tauraso,