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Some q-series identities related to divisor functions

✍ Scribed by Karl Dilcher

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 336 KB
Volume: 145
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(95)00092-b

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✦ Synopsis

The generating functions of the divisor functions adn) ---Ydl,d k are expressed as sums of products of the series U,(q):= ~ nmq" [1 (l-qJ), m= 1 ..... k+ 1, n=l j=n+l and vice versa. Other related q-series identities are derived, including

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## Abstract Let A be the incidence matrix of lines and points of the classical projective plane __PG__(2, __q__) with __q__ odd. With respect to a conic in __PG__(2, __q__), the matrix A is partitioned into 9 submatrices. The rank of each of these submatrices over __F__~__q__~, the defining field o