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Binomial coefficients involving infinite powers of primes | Donald M. Davis
; | Date: |
26 Jan 2013 | Abstract: | If p is a prime and n a positive integer, let v(n) denote the exponent of p
in n, and u(n)=n/p^{v(n)} the unit part of n. If k is a positive integer not
divisible by p, we show that the p-adic limit of (-1)^{pke} u((kp^e)!) as e
goes to infinity is a well-defined p-adic integer, which we call z_k. In terms
of these, we give a formula for the p-adic limit of binom{a p^e +c, b p^e +d)
as e goes to infinity, which we call binom(a p^infty +c, b p^infty +d). Here
a ge b are positive integers, and c and d are integers. | Source: | arXiv, 1301.6285 | Services: | Forum | Review | PDF | Favorites |
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