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.
Mittelwertsätze der Gitterpunktlehre. II.
Mittelwertsätze der Gitterpunktlehre. III
Mittlere Darstellungen natürlicher Zahlen als Summe von -ten Potenzen
New Omega Theorems for Two Classical Lattice Points Problems.
New proofs of a theorem of Edmund Landau
Nichteuklidische Gitterpunktprobleme und Gleichverteilung in linearen algebraischen Gruppen.
Nombre de points entiers dans une famille homothétique de domaines de
Normal polytopes, triangulations, and Koszul algebras.
On a certain sum in number theory. III.
On a number theoretic conjecture on positive integral points in a 5-dimensional tetrahedron and a sharp estimate of the Dickman–De Bruijn function
It is well known that getting the estimate of integral points in right-angled simplices is equivalent to getting the estimate of Dickman-De Bruijn function which is the number of positive integers and free of prime factors . Motivating from the Yau Geometry Conjecture, the third author formulated the Number Theoretic Conjecture which gives a sharp polynomial upper estimate that counts the number of positive integral points in n-dimensional () real right-angled simplices. In this paper, we...
On a Problem Connected with a Theorem of Jarnik.
On certain sum in number theory
On Estermann's proof of a theorem of Minkowski
On higher-power moments of Δ(x)
On integer points in polygons
The phenomenon of anomaly small error terms in the lattice point problem is considered in detail in two dimensions. For irrational polygons the errors are expressed in terms of diophantine properties of the side slopes. As a result, for the -dilatation, , of certain classes of irrational polygons the error terms are bounded as with some , or as with arbitrarily small .
On lattice points in large convex bodies
On primitive lattice points in planar domains