Lower and upper bounds for the number of solutions of
Lower bounds for sums of Barban-Davenport-Halberstam type.
Lp-bounds for spherical maximal operators on Zn.
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.
-rank differences for partitions without repeated odd parts
We prove formulas for the generating functions for -rank differences for partitions without repeated odd parts. These formulas are in terms of modular forms and generalized Lambert series.
M₂-rank differences for overpartitions
MacMahon's partition analysis XI: Broken diamonds and modular forms
Majorations de fonctions arithmétiques en moyenne sur des ensembles de faible densité
Maximum product over partitions into distinct parts.
Mean square limit for lattice points in a sphere
Mean square value of exponential sums related to representation of integers as sum of two squares
Mean Value Estimates in Lattice Point Theory.
Mean values of Dirichlet polynomials and applications to linear equations with prime variables
Minimal -complete partitions.
Mittelwertsätze der Gitterpunktlehre. II.
Mittelwertsätze der Gitterpunktlehre. III
Mittlere Darstellungen natürlicher Zahlen als Summe von -ten Potenzen
Mixed sums of squares and triangular numbers
Mock modular forms and singular combinatorial series
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...
Modular Forms of Half Integral Weight, Some Explicit Arithmetic.