The circle method and pairs of quadratic forms
نویسندگان
چکیده
منابع مشابه
Bailey Pairs and Indefinite Quadratic Forms
We construct classes of Bailey pairs where the exponent of q in αn is an indefinite quadratic form. As an application we obtain families of q-hypergeometric mock theta multisums.
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Let Fq be a finite field with q elements and let X be a set of matrices over Fq. The main results of this paper are explicit expressions for the number of pairs (A,B) of matrices in X such that A has rank r, B has rank s, and A + B has rank k in the cases that (i) X is the set of alternating matrices over Fq and (ii) X is the set of symmetric matrices over Fq for odd q. Our motivation to study ...
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If the coefficients r(n) satisfy suitable arithmetic conditions the behaviour of F (α) will be determined by an appropriate rational approximation a/q to α, with small values of q usually producing large values of F (α). When α lies in an interval [a/q − δ, a/q + δ] with q small, a ‘major arc’, one hopes to estimate F (α) asymptotically, while if the corresponding q is large, for the ‘minor arc...
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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2010
ISSN: 1246-7405
DOI: 10.5802/jtnb.724