ON WARING'S PROBLEM: TWO SQUARES AND THREE BIQUADRATES

John Friedlander, Trevor D. Wooley

Type: Article

Publication Date: 2013-06-28

Citations: 9

DOI: https://doi.org/10.1112/s0025579313000089

Abstract

We investigate sums of mixed powers involving two squares and three biquadrates. In particular, subject to the truth of the Generalised Riemann Hypothesis and the Elliott-Halberstam Conjecture, we show that all large natural numbers n with 8 not dividing n, n not congruent to 2 modulo 3, and n not congruent to 14 modulo 16, are the sum of 2 squares and 3 biquadrates.

Locations

arXiv (Cornell University) - View - PDF
DataCite API - View
Mathematika - View

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Action	Title	Year	Authors
+	Opera de Cribro	2010	John Friedlander Henryk Iwaniec
+	Analytic Methods for Diophantine Equations and Diophantine Inequalities	2005	H. Davenport T. D. Browning
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+	On Sums of Mixed Powers	1971	R. C. Vaughan
+	On Waring's Problem for Smaller Exponents	1986	R. C. Vaughan
+	Nonhomogeneous waring equations	1998	E. P. Golubeva
+	Sums of Squares and Higher Powers	1987	Jörg Brüdern
+ PDF Chat	A bound for the representability of large numbers by ternary quadratic forms and nonhomogeneous waring equations	2009	E. P. Golubeva
+	Sums of fourth powers and related topics	1999	Kiyokazu Kawada Trevor D. Wooley
+	A problem in additive number theory	1988	Jörg Brüdern