4 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_…
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…
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…
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 rank…