From the 1 of 6 linked papers with an AI index.
6 papers · 1 filter
Congruences for sums involving
Sandro Mattarei, Roberto Tauraso
We primarily investigate congruences modulo for finite sums of the form over the ranges and , where is a prime larger than the p…
A -analogue of the Koecher-Leshchiner generating function of odd zeta values
Roberto Tauraso
In the 1980s, Koecher and, independently, Leshchiner found an elegant formula for the generating function of odd zeta values. In this short note, we derive a -analogue of this f…
Arithmetic properties of MacMahon-type sums of divisors: the odd case
James A. Sellers, Roberto Tauraso
A century ago, P. A. MacMahon introduced two families of generating functions, $$ \sum_{1\leq n_1<n_2<\cdots<n_t}\prod_{k=1}^t\frac{q^{n_k}}{(1-q^{n_k})^2} \quad\text{ and } \sum_{…
Arithmetic properties of MacMahon-type sums of divisors
James A. Sellers, Roberto Tauraso
In this paper, we prove several new infinite families of Ramanujan--like congruences satisfied by the coefficients of the generating function which is an extension of Ma…
Further study on MacMahon-type sums of divisors
Tewodros Amdeberhan, George E. Andrews, Roberto Tauraso
This paper is devoted to the study of $$ U_t(a,q):=\sum_{1\leq n_1<n_2<\cdots<n_t}\frac{q^{n_1+n_2+\cdots+n_t}}{(1+aq^{n_1}+q^{2n_1})(1+aq^{n_2}+q^{2n_2})\cdots(1+aq^{n_t}+q^{2n_t}…
Congruences for sums of MacMahon's -Catalan polynomials
Tewodros Amdeberhan, Roberto Tauraso
One variant of the -Catalan polynomials is defined in terms of Gaussian polynomials by . Liu s…