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5 papers · 1 filter
Rank-Crank type PDE's for higher level Appell functions
Sander Zwegers
In this paper we consider level l Appell functions, and find a partial differential equation for all odd l. For l=3 this recovers the Rank-Crank PDE, found by Atkin and Garvan, and…
Rankin's method and Jacobi forms of several variables
B. Ramakrishnan, Brundaban Sahu
Following Rankin's method, D. Zagier computed the -th Rankin-Cohen bracket of a modular form of weight with the Eisenstein series of weight and then computed the…
Rank-Crank type PDE's and non-holomorphic Jacobi forms
Kathrin Bringmann, Sander Zwegers
In this paper we show how Rank-Crank type PDE's (first found by Atkin and Garvan) occur naturally in the framework of non-holomorphic Jacobiforms and find an infinite family of suc…
Multiplicative Order of Gauss Periods
Omran Ahmadi, Igor E. Shparlinski, Jose Felipe Voloch
We obtain a lower bound on the multiplicative order of Gauss periods which generate normal bases over finite fields. This bound improves the previous bound of J. von zur Gathen and…
Annihilating polynomials for quadratic forms and Stirling numbers of the second kind
Stefan A. G. De Wannemacker
We present a set of generators of the full annihilator ideal for the Witt ring of an arbitrary field of characteristic unequal to two satisfying a non-vanishing condition on the po…