4 papers
Lambert series and double Lambert series
Tewodros Amdeberhan, George E. Andrews, Cristina Ballantine
We consider relationships between classical Lambert series, multiple Lambert series and classical -series of the Rogers-Ramanujan type. We conclude with a contemplation on the A…
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}…
Hook lengths in self-conjugate partitions
Tewodros Amdeberhan, George E. Andrews, Ken Ono +1
In 2010, G.-N. Han obtained the generating function for the number of size hooks among integer partitions. Here we obtain these generating functions for self-conjugate partitio…
Extensions of MacMahon's sums of divisors
Tewodros Amdeberhan, George E. Andrews, Roberto Tauraso
In 1920, P. A. MacMahon generalized the (classical) notion of divisor sums by relating it to the theory of partitions of integers. In this paper, we extend the idea of MacMahon. In…