Bailey pairs and indefinite 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.
متن کاملQuadratic Irrationals, Quadratic Ideals and Indefinite Quadratic Forms II
Let D = 1 be a positive non-square integer and let δ = √ D or 1+ √ D 2 be a real quadratic irrational with trace t = δ + δ and norm n = δδ. Let γ = P+δ Q be a quadratic irrational for positive integers P and Q. Given a quadratic irrational γ, there exist a quadratic ideal Iγ = [Q, δ + P ] and an indefinite quadratic form Fγ(x, y) = Q(x−γy)(x−γy) of discriminant Δ = t − 4n. In the first section,...
متن کاملLifting Bailey pairs to WP-Bailey pairs
A pair of sequences (αn(a, k, q),βn(a, k, q)) such that α0(a, k, q) = 1 and βn(a, k, q) = n ∑ j=0 (k/a; q)n−j(k; q)n+j (q; q)n−j(aq; q)n+j αj(a, k, q) is termed a WP-Bailey Pair. Upon setting k = 0 in such a pair we obtain a Bailey pair. In the present paper we consider the problem of “lifting” a Bailey pair to a WPBailey pair, and use some of the new WP-Bailey pairs found in this way to derive...
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We consider some properties of indefinite binary quadratic forms F (x, y) = ax +bxy−y of discriminant ∆ = b +4a, and quadratic ideals I = [a, b−√∆ ]. AMS Mathematics Subject Classification (2000): 11E04, 11E12, 11E16
متن کاملNeighbors of Indefinite Binary Quadratic Forms
In this paper, we derive some algebraic identities on right and left neighbors R(F ) and L(F ) of an indefinite binary quadratic form F = F (x, y) = ax + bxy + cy of discriminant Δ = b − 4ac. We prove that the proper cycle of F can be given by using its consecutive left neighbors. Also we construct a connection between right and left neighbors of F . Keywords—Quadratic form, indefinite form, cy...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2014
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2013.09.009