Counting in hyperbolic spikes: the diophantine analysis of multihomogeneous diagonal equations
Number Theory
2014-02-06 v1
Abstract
A method is described to sum multi-dimensional arithmetic functions subject to hyperbolic summation conditions, provided that asymptotic formulae in rectangular boxes are available. In combination with the circle method, the new method is a versatile tool to count rational points on algebraic varieties defined by multi-homogeneous diagonal equations.
Keywords
Cite
@article{arxiv.1402.1122,
title = {Counting in hyperbolic spikes: the diophantine analysis of multihomogeneous diagonal equations},
author = {Valentin Blomer and Jörg Brüdern},
journal= {arXiv preprint arXiv:1402.1122},
year = {2014}
}
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42 pages