49 citations · 203 across the 42 of their papers we have counts for
47 papers
Franklin's identity for -color partitions and companion Beck-type identities
Cristina Ballantine, Roberto Tauraso
We show that some classical identities valid for ordinary partitions have precise analogues for -color partitions, that is partitions in which a part of size can occur…
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, $$ \sum_{1\leq n_1<n_2<\cdots<n_t}\prod_{k=1}^t\frac{q^{n_k}}{(1-q^{n_k})^2} \quad\text{ and } \sum_{…
Congruences for sums involving
Sandro Mattarei, Roberto Tauraso
We primarily investigate congruences modulo for finite sums of the form over the ranges and , where is a prime larger than the p…
Arithmetic properties of MacMahon-type sums of divisors
James A. Sellers, Roberto Tauraso
In this paper, we prove several new infinite families of Ramanujan--like congruences satisfied by the coefficients of the generating function which is an extension of Ma…
Further study on MacMahon-type sums of divisors
Tewodros Amdeberhan, George E. Andrews, Roberto Tauraso
This paper is devoted to the study of $$ 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}…