Über eine Vermutung von Choi, Erdös und Nathanson
Über Mittelwerte trigonometrischer Summen und ihre Anwendung in algebraischen Zahlkörpern.
Über Zerlegungen in n-te Potenzen mit lauter verschiedenen Grundzahlen
Une fonction arithmétique liée aux sommes de deux carrés.
Une généralisation du problème de Waring-Goldbach polynomial
Une présentation adélique de la série singulière et du problème de Waring
Universal forms and Waring’s problem
Untere Abschätzung für die Anzahl der B-Zwillinge auf kurzen Intervallen
Variations sur un thème de Siegel et Hecke
Variations sur un thème de Siegel-Hecke.
Variations sur un thème de Siegel-Hecke
Verzichtbare und unverzichtbare Elemente bei der Darstellung als Summe und als Differenz von Quadraten
Von Polyedern im ganzzahligen Gitter.
Waring's number for large subgroups of ℤ*ₚ*
Let p be a prime, ℤₚ be the finite field in p elements, k be a positive integer, and A be the multiplicative subgroup of nonzero kth powers in ℤₚ. The goal of this paper is to determine, for a given positive integer s, a value tₛ such that if |A| ≫ tₛ then every element of ℤₚ is a sum of s kth powers. We obtain , and for s ≥ 6, . For s ≥ 24 further improvements are made, such as and .
Waring’s problem for Beatty sequences and a local to global principle
We investigate in various ways the representation of a large natural number as a sum of positive -th powers of numbers from a fixed Beatty sequence. Inter alia, a very general form of the local to global principle is established in additive number theory. Although the proof is very short, it depends on a deep theorem of M. Kneser.
Waring’s problem for [Book]
Waring's problem for fields
If K is a field, denote by P(K,k) the a ∈ K which are sums of kth powers of elements of K, by P⁺(K,k) the set of a ∈ K which are sums of kth powers of totally positive elements of K. We give some simple conditions for which there exist integers w(K,k) and g(K,k) such that: a ∈ P(K,k) implies that a is the sum of at most w(K,k) kth powers; a ∈ P⁺(K,k) implies that a is the sum of at most g(K,k) totally positive kth powers. We apply the results to characterise functions that are sums of kth powers...
Waring's problem for polynomial cubes and squares over a finite field with odd characteristic.
Waring's problem for sixteen biquadrates. Numerical results
We explain the algorithms that we have implemented to show that all integers congruent to modulo in the interval are sums of five fourth powers, and that all integers congruent to or modulo in the interval are sums of seven fourth powers. We also give some results related to small sums of biquadrates. Combining with the Dickson ascent method, we deduce that all integers in the interval are sums of biquadrates.
Waring's problem in GF(q,x)