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Counting in hyperbolic spikes: The diophantine analysis of multihomogeneous diagonal equations

  • Published:2018-04-01 Issue:737 Volume:2018 Page:255-300
  • ISSN:0075-4102
  • Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
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Author:

Blomer Valentin,Brüdern Jörg

Abstract

AbstractA 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.

Funder

Volkswagen Foundation

European Research Council

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

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