An instance where the major and minor arc integrals meet

Jörg Brüdern, Trevor D. Wooley

Type: Article

Publication Date: 2019-10-31

Citations: 2

DOI: https://doi.org/10.1112/blms.12291

Abstract

We apply the circle method to obtain an asymptotic formula for the number of integral points on a certain sliced cubic hypersurface related to the Segre cubic. Unusually, the major and minor arc integrals in this application are both positive and of the same order of magnitude.

Locations

Bulletin of the London Mathematical Society - View - PDF
arXiv (Cornell University) - View - PDF
Bristol Research (University of Bristol) - View - PDF
DataCite API - View

Similar Works

Action	Title	Year	Authors
+	Trace Formula for Integral Points on the Three-Dimensional Sphere	2020	В. А. Быковский M. D. Monina
+ PDF Chat	The integer points in a plane curve	2007	M. N. Huxley
+	A Graceful Formula on the Number of Integral Points	2006	Haicheng Ma
+ PDF Chat	The proportion of plane cubic curves over ℚ that everywhere locally have a point	2015	Manjul Bhargava J. E. Cremona Tom Fisher
+	The Manin–Peyre conjecture for certain multiprojective hypersurfaces	2024	Xiaodong Zhao
+	On a certain non-split cubic surface	2017	Régis de la Bretèche Jianya Liu Jie Wu Yongqiang Zhao
+	The Moser's formula for the division of the circle by chords problem revisited	2017	Carlos Rodriguez-Lucatero
+ PDF Chat	AN INTEGRAL FORMULA AND ITS APPLICATIONS	2002	Y.D. Chai Moonjeong Kim
+	Integral points on convex curves	2018	Jean-Marc Deshouillérs Adrián Ubis
+ PDF Chat	Integral points on convex curves	2020	Jean-Marc Deshouillérs Adrián Ubis
+	Manin’s conjecture for a class of singular cubic hypersurfaces	2021	Wenguang Zhai
+ PDF Chat	Integral points on convex curves	2020	Jean-Marc Deshouillérs Adrián Ubis
+	Integral formulas in Crofton’s style on the sphere and some inequalities referring to spherical curves	1942	Lluís Santaló
+	The proportion of plane cubic curves over ${\mathbb Q}$ that everywhere locally have a point	2013	Manjul Bhargava J. E. Cremona Tom Fisher
+	Upper Bounds for the Number of Integral Points on Quadratic Curves and Surfaces	2010	Veronika Shelestunova
+	The number of integral points in integral polyhedra	1977	D. N. Bernshtein
+	An estimate for the number of integral points on certain surfaces of second order	1982	R. Babaeva
+	The trisecant formula and hyperelliptic surfaces	1992	Hershel M. Farkas
+	Uniform bounds for rational points on cubic hypersurfaces	2015	Per Salberger
+	Corrigendum to: Maximal open radius for Strebel point	2016	Guowu Yao

Works That Cite This (2)

Action	Title	Year	Authors
+ PDF Chat	A paucity problem for certain triples of diagonal equations	2022	Jörg Brüdern Trevor D. Wooley
+	Isolating special solutions in the delta method: The case of a diagonal cubic equation in evenly many variables over $\mathbb{Q}$	2021	Victor Y. Wang

Works Cited by This (19)

Action	Title	Year	Authors
+	Analytic Methods for Diophantine Equations and Diophantine Inequalities	2005	H. Davenport T. D. Browning
+	Torseurs Universels Et Méthode Du Cercle	2001	Emmanuel Peyre
+ PDF Chat	Mean value estimates for odd cubic Weyl sums	2015	Trevor D. Wooley
+	Additive Theory of Prime Numbers	2009	Hua Liu
+ PDF Chat	Rational points on linear slices of diagonal hypersurfaces	2015	Jörg Brüdern Olivier Robert
+	Rational points of bounded height on Fano varieties	1989	Jens Frankē Yuri I. Manin Yuri Tschinkel
+	Sur le nombre des points rationnels de hauteur borné des variétés algébriques	1990	Victor V. Batyrev Yu. I. Manin
+	On a certain nonary cubic form and related equations	1995	R. C. Vaughan Trevor D. Wooley
+ PDF Chat	The density of integer points on homogeneous varieties	1985	Wolfgang M. Schmidt
+	Hauteurs et mesures de Tamagawa sur les variétés de Fano	1995	Emmanuel Peyre