5 papers · 1 filter
On a conjecture of Andrews and almost alternating sign patterns
Jayashree Kalita, Debanjana Kundu, Matthias Storzer +1
In this paper, we prove a sign phenomenon first observed by Andrews for certain -series from Ramanujan's Lost Notebook. For three of the series considered by Andrews, namely $v_…
Bailey pairs, Eichler integrals and unified Witten-Reshetikhin-Turaev invariants
Jeremy Lovejoy, Robert Osburn, Matthias Storzer
In 1999, Lawrence and Zagier expressed the Witten-Reshetikhin-Turaev (WRT) invariant of the Poincaré homology sphere as the limiting value of the Eichler integral of a weight 3/2 m…
Generalized rank deviations for overpartitions
Kevin Allen, Robert Osburn, Matthias Storzer
We prove formulas for generalized rank deviations for overpartitions. These formulas are in terms of Appell-Lerch series and sums of quotients of theta functions and extend work of…
Asymptotics of parity biases for partitions into distinct parts via Nahm sums
Kathrin Bringmann, Siu Hang Man, Larry Rolen +1
For a random partition, one of the most basic questions is: what can one expect about the parts which arise? For example, what is the distribution of the parts of random partitions…
Oscillating asymptotics and conjectures of Andrews
Amanda Folsom, Joshua Males, Larry Rolen +1
In 1986, Andrews studied the function from Ramanujan's ``Lost" Notebook, and made several conjectures on its Fourier coefficients , which count certain partition ranks…