Arithmetic theory of harmonic numbers
Author:
ZhiWei Sun
Journal:
Proc. Amer. Math. Soc. 140 (2012), 415428
MSC (2010):
Primary 11B75; Secondary 05A19, 11A07, 11B68
Published electronically:
June 8, 2011
MathSciNet review:
2846311
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Additional Information
Abstract: Harmonic numbers play important roles in mathematics. In this paper we investigate their arithmetic properties and obtain various basic congruences. Let be a prime. We show that and (In contrast, it is known that and .) Our tools include some sophisticated combinatorial identities and properties of Bernoulli numbers.
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 [ASVZ]
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 [B]
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 [BPQ]
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Additional Information
ZhiWei Sun
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China
Email:
zwsun@nju.edu.cn
DOI:
http://dx.doi.org/10.1090/S000299392011109250
PII:
S 00029939(2011)109250
Keywords:
Harmonic numbers,
congruences,
Bernoulli numbers
Received by editor(s):
July 22, 2010
Received by editor(s) in revised form:
November 23, 2010
Published electronically:
June 8, 2011
Additional Notes:
The author was supported by the National Natural Science Foundation (grant 10871087) of China
Communicated by:
Matthew A. Papanikolas
Article copyright:
© Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
