Generalized harmonic morphisms and horizontally weakly conformal biharmonic maps
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DOI: 10.1016/j.jmaa.2018.04.044
Abstract: Harmonic morphisms are maps between Riemannian manifolds that pull back harmonic functions to harmonic functions. These maps are characterized as horizontally weakly conformal harmonic maps and they have many interesting links and applications to several… read more here.
Keywords: harmonic functions; weakly conformal; generalized harmonic; horizontally weakly ... See more keywords
A congruence for some generalized harmonic type sums
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DOI: 10.1142/s1793042118500628
Abstract: In 1862, Wolstenholme proved that the numerator of the (p − 1)th harmonic number is divisible by p2 for any prime p ≥ 5. A variation of this theorem was shown by Alkan and Leudesdorf.… read more here.
Keywords: generalized harmonic; type sums; harmonic type; congruence generalized ... See more keywords
Generalized harmonic number sums and quasisymmetric functions
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DOI: 10.1216/rmj.2020.50.1253
Abstract: We express some general type of infinite series such as $$ \sum^\infty_{n=1}\frac{F(H_n^{(m)}(z),H_n^{(2m)}(z),\ldots,H_n^{(\ell m)}(z))} {(n+z)^{s_1}(n+1+z)^{s_2}\cdots (n+k-1+z)^{s_k}}, $$ where $F(x_1,\ldots,x_\ell)\in\mathbb Q[x_1,\ldots,x_\ell]$, $H_n^{(m)}(z)=\sum^n_{j=1}1/(j+z)^m$, $z\in (-1,0]$, and $s_1,\ldots,s_k$ are nonnegative integers with $s_1+\cdots+s_k\geq 2$, as a linear combination of… read more here.
Keywords: sums quasisymmetric; number sums; ldots ell; quasisymmetric functions ... See more keywords
Some identities on generalized harmonic numbers and generalized harmonic functions
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DOI: 10.1515/dema-2022-0229
Abstract: Abstract The harmonic numbers and generalized harmonic numbers appear frequently in many diverse areas such as combinatorial problems, many expressions involving special functions in analytic number theory, and analysis of algorithms. The aim of this… read more here.
Keywords: harmonic numbers; harmonic functions; generalized harmonic; identities generalized ... See more keywords