For $m\in $, $(m,6)=1$, it is proved the relations between the sums \[ W(m,s)=\sum _{i=1, (i,m)=1}^{m-1} i^{-s}\,, \quad \quad s\in \,, \] and Bernoulli numbers. The result supplements the known theorems of C. Leudesdorf, N. Rama Rao and others. As the application it is obtained some connections between the sums $W(m,s)$ and Agoh’s functions, Wilson quotients, the indices irregularity of Bernoulli numbers.
@article{107704,
author = {I. Sh. Slavutsky},
title = {Leudesdorf's theorem and Bernoulli numbers},
journal = {Archivum Mathematicum},
volume = {035},
year = {1999},
pages = {299-303},
zbl = {1053.11003},
mrnumber = {1744517},
language = {en},
url = {http://dml.mathdoc.fr/item/107704}
}
Slavutsky, I. Sh. Leudesdorf's theorem and Bernoulli numbers. Archivum Mathematicum, Tome 035 (1999) pp. 299-303. http://gdmltest.u-ga.fr/item/107704/
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