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THE p-ADIC GROWTH OF HARMONIC SUMS The numbers Hn =1+
THE p-ADIC GROWTH OF HARMONIC SUMS. KEITH CONRAD. The numbers. Hn =1+. 1. 2. + ··· +. 1 n. = n. ∑ k=1. 1 k are called harmonic sums. Integrals can ...

A p-adic Study of the Partial Sums of the Harmonic - Project Euclid
A p-adic Study of the Partial Sums of the Harmonic Series. David W. Boyd. CONTENTS. 1. Introduction. 2. Some Preliminary Material. 3. Recursive Generation of ...
1048515811

The arithmetic of multiple harmonic sums - University of Michigan
3.2.3 p-adic L-function values in terms of multiple harmonic sums . . . . 52 ... Formal p-adic Identities Among Multiple Harmonic Sums . . . . . . . . . . 61. 4.1 Multiple ...
julian_rosen.pdf

A proof of a simple conjecture about harmonic numbers
Feb 3, 2011 ... where the innermost sum is divisible by p as a consequence of ...  David W. Boyd, A p-adic Study of the Partial Sums of the Harmonic Series,.
0fcfd51113390968a1000000.pdf

Multiple harmonic sums and Wolstenholme's theorem
Feb 1, 2013 ... multiple harmonic sums H({1}j; p−1) (with p fixed) satisfies a ....  we will show that there is a parallel family of congruences related to p-adic.
1302.0073

p-Integral harmonic sums - ScienceDirect
When J(p) = (0, p - 1, p(p - 1), p2 - 1), the prime p is called harmonic. Many small primes ... (k.n>=ik (2.1) p-Integral harmonic sums 251 we have H(n) = H*(n) + p H (ñ). (2.2) Let QP ..... On the p-adic valuation of harmonic numbers. 2016, Journal  ...
1-s2.0-0012365X90902349-main.pdf?_tid=1ca64cf4-0f83-11e5-a368-00000aacb362&acdnat=1433949330_79d53a1194be5a2b687b970d14a21e6a

ON 3-ADIC VALUATIONS OF GENERALIZED HARMONIC - Integers
Nov 7, 2011 ... rational number x, we denote the p-adic order of x by vp(x) and use the .... The alternating harmonic series is a simple analogy of the harmonic ...
l69.pdf

Congruences involving alternating multiple harmonic sums
Jan 14, 2010 ... Let p be a prime number, what is the p-adic analogue of the above result? ... ( mod p). 2 Alternating multiple harmonic sums. Let r > 0 and let (a1 ...
v17i1r16.pdf

THE p–ADIC ORDER OF POWER SUMS - Department of Mathematics
For q ∈ Z and prime p, the p-adic order of q is the exponent vp(q) of the highest power of .... Fixing a prime p, we define the restricted power sum S∗ n(0) := 0 ...
Sondow_Tsukerman_EME1.1.14.pdf

Wolstenholme's theorem: Its Generalizations and Extensions in the
Dec 25, 2011 ... n = n0 + n1p + ···+ nsps and m = m0 + m1p + ···+ msps are the p-adic ... is devoted to the Wolstenholme's type harmonic series congruences.
Wolstenholme_theorem____ROMEO_MESTROVIC__1111.3057.pdf

Aug 23, 2012 ... Fundamental congruences for harmonic numbers. Z. W. Sun (2009) [Proc. .... Part C. p-adic Congruences from π-series or the ζ-function. 16 / 48 ...
p-Cong.pdf

arXiv:math/0605703v1 [math.NT] 27 May 2006 - arXiv.org
May 27, 2006 ... The purpose of this paper is to give alternating p-adic harmonic series in terms of n and p-adic l-function for Euler numbers. 2. A note on l-series ...
0605703.pdf

Distribution of Harmonic Sums and Bernoulli Polynomials Modulo a
and Hs(n) is computed modulo p for 0 ≤ M<M + N<p. Here we use our ... modulo p be represented as a sum of harmonic sums in the same range as above (and .....  A. M. Robert, A course in p-adic analysis, Springer, NY, 2000.  A. Weil  ...
Harmonic.pdf

GAUSSIAN HYPERGEOMETRIC SERIES AND
Apr 29, 2008 ... eralized Harmonic sum identities discovered using the computer .... formula  to express the Gauss sums in terms of p-adic Gamma functions ...
S0025-5718-08-02118-2.pdf

PDF file
P-integral to the problem of recovering the coefficients of series with respect ... In the case of the dyadic harmonic analysis and its P-adic generalization, a role.
amapn20_25.pdf

ON THE ADDITIVE STRUCTURE OF Qp AND THE NATURE OF p
Aug 22, 2011 ... understanding properties of p-adic power series. We begin by defining ... This leads us into an analysis of p-adic sequences, series, and power ...
Pailoor.pdf

MULTIVARIATE p-ADIC FORMAL CONGRUENCES - Institut Fourier
Items 1 - 29 ... (D3) a reduction lemma for harmonic numbers due to the authors (cf. ... eralised p -adic hypergeometric series in one variable, we expect our result ...
mirrormult.pdf

p-ADIC PROPERTIES OF MAASS FORMS ARISING FROM THETA
Apr 18, 2007 ... harmonic weak Maass forms of weight 1/2 and 3/2. Each of the forms in ... sum of a holomorphic function and a period integral of a theta series.
MRL-2008-0015-0003-a006.pdf