Birch's theorem with shifts

Sam Chow

Research output: Contribution to journalArticle (Academic Journal)peer-review

122 Downloads (Pure)


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 languageEnglish
Pages (from-to)449-483
Number of pages35
JournalAnnali della Scuola Normale Superiore di Pisa - Classe di Scienze
Issue number2
Publication statusPublished - 19 Jun 2017


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