Abstract
AbstractWe prove general fomulas for the deviations of two overpartition ranks from the average. These formulas are in terms of Appell–Lerch series and sums of quotients of theta functions and can be used, among other things, to recover any of the numerous overpartition rank difference identities in the literature. We give two illustrations.
Publisher
Springer Science and Business Media LLC
Reference29 articles.
1. Bian, M., Fang, H., Huang, X.Q., Yao, O.X.M.: Ranks, cranks for overpartitions and Appell-Lerch sums. Ramanujan J. 57(2), 823–844 (2022)
2. Bringmann, K., Lovejoy, J.: Dyson’s rank, overpartitions, and weak Maass forms. Int. Math. Res. Not. IMRN no. 19, Art. ID rnm063 (2007)
3. Bringmann, K., Lovejoy, J.: Overpartitions and class numbers of binary quadratic forms. Proc. Natl. Acad. Sci. USA 106(14), 5513–5516 (2009)
4. Bringmann, K., Ono, K.: Dyson’s ranks and Maass forms. Ann. of Math. 171(1), 419–449 (2010)
5. Bringmann, K., Ono, K., Rhoades, R.C.: Eulerian series as modular forms. J. Amer. Math. Soc. 21(4), 1085–1104 (2008)