12 papers · 1 filter
Quasimodular forms arising from Jacobi's theta function and special symmetric polynomials
Tewodros Amdeberhan, Leonid G. Fel, Ken Ono
Ramanujan derived a sequence of even weight quasimodular forms from derivatives of Jacobi's weight theta function. Using the generating function for this seq…
Some topological genera and Jacobi forms
Tewodros Amdeberhan, Michael Griffin, Ken Ono
We revisit and elucidate the -genus, Hirzebruch's -genus and Witten's -genus, cobordism invariants of special classes of manifolds. After slight modification, in…
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…
From crank to congruences
Tewodros Amdeberhan, Mircea Merca
In this paper, we investigate the arithmetic properties of the difference between the number of partitions of a positive integer with even crank and those with odd crank, denot…
On the -adic valuations of values of Legendre polynomials
Max A. Alekseyev, Tewodros Amdeberhan, Jeffrey Shallit +1
We prove an explicit formula for the -adic valuation of the Legendre polynomials evaluated at a prime , and generalize an old conjecture of the third author. We also…
Traces of partition Eisenstein series
Tewodros Amdeberhan, Michael Griffin, Ken Ono +1
We study "partition Eisenstein series", extensions of the Eisenstein series defined by $$λ=(1^{m_1}, 2^{m_2},\dots, k^{m_k}) \vdash k \ \ \ \ \ \longmapsto \ \ \ \ \…