Hardy-Littlewood varieties and semisimple groups | Zendy

Mikhail Borovoi | Zendy; Ze�v Rudnick | Zendy

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Hardy-Littlewood varieties and semisimple groups

Author(s) -

Mikhail Borovoi,

Ze�v Rudnick

Publication year - 1995

Publication title -

inventiones mathematicae

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 5.536

H-Index - 125

eISSN - 1432-1297

pISSN - 0020-9910

DOI - 10.1007/bf01245174

Subject(s) - mathematics , pure mathematics , affine transformation , variety (cybernetics) , homogeneous , congruence (geometry) , algebraic number , affine variety , algebraic group , algebraic variety , combinatorics , mathematical analysis , geometry , statistics

Summary We are interested in counting integer and rational points in affine algebraic varieties, also under congruence conditions. We introduce the notions of a strongly Hardy-Littlewood variety and a relatively Hardy-Littlewood variety, in terms of counting rational points satisfying congruence conditions. The definition of a strongly Hardy-Littlewood variety is given in such a way that varieties for which the Hardy-Littlewood circle method is applicable are strongly Hardy-Littlewood.

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