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Lp-bounds for spherical maximal operators on Zn.

Akos Magyar (1997)

Revista Matemática Iberoamericana

We prove analogue statements of the spherical maximal theorem of E. M. Stein, for the lattice points Zn. We decompose the discrete spherical measures as an integral of Gaussian kernels st,ε(x) = e2πi|x|2(t + iε). By using Minkowski's integral inequality it is enough to prove Lp-bounds for the corresponding convolution operators. The proof is then based on L2-estimates by analysing the Fourier transforms ^st,ε(ξ), which can be handled by making use of the circle method for exponential sums. As a...

Lucas partitions.

Robbins, Neville (1998)

International Journal of Mathematics and Mathematical Sciences

M 2 -rank differences for partitions without repeated odd parts

Jeremy Lovejoy, Robert Osburn (2009)

Journal de Théorie des Nombres de Bordeaux

We prove formulas for the generating functions for M 2 -rank differences for partitions without repeated odd parts. These formulas are in terms of modular forms and generalized Lambert series.

Mock modular forms and singular combinatorial series

Amanda Folsom, Susie Kimport (2013)

Acta Arithmetica

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...

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