Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Mock modular forms and singular combinatorial series

100%

Folsom A., Kimport S.

Acta Arithmetica

2013

tom 159

nr 3

257-297

A celebrated result of Bringmann and Ono shows that the combinatorial rank generating function exhibits automorphic properties after being completed by the addition of a non-holomorphic integral. Since then, automorphic properties of various related combinatorial families have been studied. Here, extending work of Andrews and Bringmann, we study general infinite families of combinatorial q-series pertaining to k-marked Durfee symbols, in which we allow additional singularities. We show that these singular combinatorial families are essentially mixed mock and quasimock modular forms, and provide their explicit non-holomorphic completions. As a special case of our work, we consider k=3, and provide an asymptotic expansion for the associated partition rank statistic, solving a special case of an open problem of Andrews.

On a quantitative refinement of the Lagrange spectrum

71%

Burger E., Folsom A., Pekker A., Roengpitya R., Snyder J.

Acta Arithmetica

2002

tom 102

nr 1

55-82

Ograniczanie wyników

2 Acta Arithmetica

2 Folsom A.

1 Burger E.

1 Kimport S.

1 Pekker A.

1 Roengpitya R.

1 Snyder J.

1 2013

1 2002

Wyniki wyszukiwania

Mock modular forms and singular combinatorial series

On a quantitative refinement of the Lagrange spectrum