Waring's Problem for Fields
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)
Waring's problem in quadratic number fields
Waring's problem in quadratic number fields. Addendum
Waring's problem with small prime factors
Weak asymptotic formulas for partitions free of small summands
Weak Convergence of Probability nets on the Integers and the Erdos-Wintner Theorem as a Three Series Theorem
Weighted lattice points in threedimensional convex bodies and the number of lattice points in parts of elliptic paraboloids.
Wild partitions and number theory.
Zahlentheoretische Funktionen für die Zerteilung der Nummer in Summanden;
Zeta-Functions of Binary Hermitian Forms and Special Values of Eisenstein Series on Three-Dimensional Hyperbolic Space.
Zu einem hyperbolischen Gitterpunktproblem.
Zu einem hyperbolischen Gitterpunktproblem (Berichtigung, Zusatz).
Zu einer Aufgabe der Kombinatorik.
Zu einer Vermutung von Rohrbach.
Zum Ellipsoidproblem in algebraischen Zahlkörpern