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math.NT2012
The Zagier modification of Bernoulli numbers and a polynomial extension. Part I
Atul Dixit, Victor H. Moll, Christophe Vignat
The modified B_{n}^{*} = \sum_{r=0}^{n} \binom{n+r}{2r} \frac{B_{r}}{n+r}, \quad n > 0 introduced by D. Zagier in 1998 are extended to the polynomial case by replacing by t…
math.NT2012★ 1 cited
Generalized higher order spt-functions
Atul Dixit, Ae Ja Yee
We give a new generalization of the spt-function of G.E. Andrews, namely , and give its combinatorial interpretation in terms of successive lower-Durfee squares.…
math.NT2012
Rank-Crank type PDEs and generalized Lambert series identities
Song Heng Chan, Atul Dixit, Frank G. Garvan
We show how Rank-Crank type PDEs for higher order Appell functions due to Zwegers may be obtained from a generalized Lambert series identity due to the first author. Special cases…