Algebra & Number Theory
- Algebra Number Theory
- Volume 6, Number 5 (2012), 1019-1041.
Squareful numbers in hyperplanes
Let . In this article, we will determine the asymptotic behavior of the size of the set of integral points on the hyperplane in such that is squareful (an integer is called squareful if the exponent of each prime divisor of is at least two) and for each , when goes to infinity. For this, we will use the classical Hardy–Littlewood method. The result obtained supports a possible generalization of the Batyrev–Manin program to Fano orbifolds.
Algebra Number Theory, Volume 6, Number 5 (2012), 1019-1041.
Received: 3 December 2010
Revised: 17 June 2011
Accepted: 19 July 2011
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11D45: Counting solutions of Diophantine equations
Secondary: 14G05: Rational points 11D72: Equations in many variables [See also 11P55] 11P55: Applications of the Hardy-Littlewood method [See also 11D85]
Van Valckenborgh, Karl. Squareful numbers in hyperplanes. Algebra Number Theory 6 (2012), no. 5, 1019--1041. doi:10.2140/ant.2012.6.1019. https://projecteuclid.org/euclid.ant/1513729844