Birch's theorem with shifts

Sam Chow

doi:10.2422/2036-2145.201510_008

Birch's theorem with shifts

Sam Chow

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Abstract

A famous result due to Birch (1961) provides an asymptotic formula for the number of integer points in an expanding box at which given rational forms of the same degree simultaneously vanish, subject to a geometric condition. We present the first inequalities analogue of Birch’s theorem.

Original language	English
Pages (from-to)	449-483
Number of pages	35
Journal	Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Volume	XVII
Issue number	2
DOIs	https://doi.org/10.2422/2036-2145.201510_008
Publication status	Published - 19 Jun 2017

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abstract = "A famous result due to Birch (1961) provides an asymptotic formula for the number of integer points in an expanding box at which given rational forms of the same degree simultaneously vanish, subject to a geometric condition. We present the first inequalities analogue of Birch{\textquoteright}s theorem.",

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M3 - Article (Academic Journal)

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JF - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Birch's theorem with shifts

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