Birch's theorem with shifts

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JournalAnnali della Scuola Normale Superiore di Pisa. Classe di Scienze
DateAccepted/In press - 18 Jan 2016
DatePublished (current) - 19 Jun 2017
Pages (from-to)449-483
Original languageEnglish


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.

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    Research areas

  • diophantine inequalities, forms in many variables, inhomogeneous polynomials

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