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Mittelwerte zahlentheoretischer Funktionen und lineare Kongruenzsysteme.

Lutz Lucht (1979)

Journal für die reine und angewandte Mathematik

Mod $p$ structure of alternating and non-alternating multiple harmonic sums

Jianqiang Zhao (2011)

Journal de Théorie des Nombres de Bordeaux

The well-known Wolstenholme’s Theorem says that for every prime $p > 3$ the $(p - 1)$ -st partial sum of the harmonic series is congruent to $0$ modulo $p^{2}$ . If one replaces the harmonic series by $\sum_{k \geq 1} 1 / n^{k}$ for $k$ even, then the modulus has to be changed from $p^{2}$ to just $p$ . One may consider generalizations of this to multiple harmonic sums (MHS) and alternating multiple harmonic sums (AMHS) which are partial sums of multiple zeta value series and the alternating Euler sums, respectively. A lot of results along this direction...

Displaying 1 – 6 of 6

Mittelwerte zahlentheoretischer Funktionen und lineare Kongruenzsysteme.

Mod $p$ structure of alternating and non-alternating multiple harmonic sums

Mod p³ analogues of theorems of Gauss and Jacobi on binomial coefficients

Monomial Congruences.

Multidimensional covering systems of congruences

Multiplicative polynomials and Fermat's little theorem for non-primes.

Currently displaying 1 – 6 of 6

Displaying 1 – 6 of 6

Mittelwerte zahlentheoretischer Funktionen und lineare Kongruenzsysteme.

Mod p structure of alternating and non-alternating multiple harmonic sums

Mod p³ analogues of theorems of Gauss and Jacobi on binomial coefficients

Monomial Congruences.

Multidimensional covering systems of congruences

Multiplicative polynomials and Fermat's little theorem for non-primes.

Currently displaying 1 – 6 of 6

Mod $p$ structure of alternating and non-alternating multiple harmonic sums