Sum-product estimates applied to Waring's problem mod .
Cochrane, Todd, Pinner, Christopher (2008)
Integers
Jean-Marc Deshouillers, François Dress (1992)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
T.Y. Lam, A. Prestel, M.D. Choi (1996)
Mathematische Zeitschrift
Mireille Car, Luis Gallardo (2004)
Acta Arithmetica
R.C. Baker, J. Brüdern (1991)
Monatshefte für Mathematik
R.C. Baker, J. Brüdern (1991)
Monatshefte für Mathematik
Paul T. Bateman, Adolf J. Hildebrand, George B. Purdy (1994)
Acta Arithmetica
Koichi Kawada, Trevor D. Wooley (1998)
Acta Arithmetica
Jörg Brüdern (1989)
Monatshefte für Mathematik
Ted Chinburg, Melvin Henriksen (1976)
Acta Arithmetica
Jean-Marc Deshouillers, François Hennecart, Bernard Landreau (1998)
Acta Arithmetica
Erdős and Rényi proposed in 1960 a probabilistic model for sums of s integral sth powers. Their model leads almost surely to a positive density for sums of s pseudo sth powers, which does not reflect the case of sums of two squares. We refine their model by adding arithmetical considerations and show that our model is in accordance with a zero density for sums of two pseudo-squares and a positive density for sums of s pseudo sth powers when s ≥ 3. Moreover, our approach supports a conjecture of...
Jagy, William C., Kaplansky, Irving (1995)
Experimental Mathematics
Fernando Chamizo (1997)
Journal de théorie des nombres de Bordeaux
Gaël Collinet (2016)
Acta Arithmetica
We prove that in a ring of S-integers containing 1/2, any totally positive element is a sum of five squares. We also exhibit examples of such rings where some totally positive elements cannot be written as the sum of four squares.
Trevor D. Wooley (2015)
Acta Arithmetica
Estimates are provided for sth moments of cubic smooth Weyl sums, when 4 ≤ s ≤ 8, by enhancing the author's iterative method that delivers estimates beyond classical convexity. As a consequence, an improved lower bound is presented for the number of integers not exceeding X that are represented as the sum of three cubes of natural numbers.
Antal Balog, Brüdern Jörg (1995)
Journal für die reine und angewandte Mathematik
Hardy, J.T. (1981)
Portugaliae mathematica
C.M. Skinner, T.D. Wooley (1995)
Journal für die reine und angewandte Mathematik
Bjorn Poonen (2004)
Acta Arithmetica
Edm. Maillet (1908)
Bulletin de la Société Mathématique de France