The Generalized Divisor Problem Over Arithmetic Progressions.
The geometry of the third moment of exponential sums
We give a geometric interpretation (and we deduce an explicit formula) for two types of exponential sums, one of which is the third moment of Kloosterman sums over of type . We establish a connection between the sums considered and the number of -rational points on explicit smooth projective surfaces, one of which is a surface, whereas the other is a smooth cubic surface. As a consequence, we obtain, applying Grothendieck-Lefschetz theory, a generalized formula for the third moment of Kloosterman...
The greatest prime factor of the integers in an interval
The hybrid mean value of Dedekind sums and two-term exponential sums
In this paper, we use the mean value theorem of Dirichlet L-functions, the properties of Gauss sums and Dedekind sums to study the hybrid mean value problem involving Dedekind sums and the two-term exponential sums, and give an interesting identity and asymptotic formula for it.
The Jacobi Sums of Orders Thirteen and Sixty and Related Quadratic Decompositions.
The moments of infinite series.
The triplication formula for Gauss sums.
Trigonometrische Reihen über multiplikativen Zahlenmengen.
Über allgemeine Sequenzen der Länge 3 von Legendresymbolen.
Über die mittlere Verteilung der Werte zahlentheoretischer Funktionen auf Bestklassen. I.
Über die Wirksamkeit einiger Abschätzungen trigonometrischer Summen
Über eine Riemannsche Identität
Über einige trigonometrische Summen
Über Mittelwerte trigonometrischer Summen und ihre Anwendung in algebraischen Zahlkörpern.
Un exemple d'utilisation de la méthode de Vinogradov
Un problème binaire en théorie additive
Upper bounds for certain trigonometric sums involving cosine powers
We establish upper bounds for certain trigonometric sums involving cosine powers. Part of these results extend previous ones valid for the sum . We apply our results to estimate character sums in an explicit and elementary way.
Vector-covering systems of arithmetic sequences
Vinogradov's mean value theorem.
Weighted lattice points in threedimensional convex bodies and the number of lattice points in parts of elliptic paraboloids.