English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

In this paper we present some new identities of hypergeometric type formultiple harmonic sums whose indices are the sequences $(\{1\}^a,c,\{1\}^b),$$(\{2\}^a,c,\{2\}^b)$ and prove a number of congruences for these sums modulo aprime $p.$ The congruences obtained allow us to find nice $p$-analogues ofLeshchiner's series for zeta values and to refine a result due to M. Hoffmanand J. Zhao about the set of generators of the multiple harmonic sums of weight7 and 9 modulo $p$. Moreover, we are also able to provide a new proof ofZagier's formula for $\zeta^{*}(\{2\}^a,3,\{2\}^b)$ based on a finite identityfor partial sums of the zeta-star series.

New properties of multiple harmonic sums modulo $p$ and $p$-analogues of Leshchiner's series