A multi-variable theta product
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- 作者：Bruce C. Berndt ; Alex ; ru Zaharescu
- 关键词：F-regular subsets ; complex projective space ; shape invariant of a triangle ; equi-isoclinic planes in Euclidean spaces
- 刊名：Indagationes Mathematicae
- 出版年：2002
- 出版时间：25 March 2002
- 年：2002
- 卷：13
- 期：1
- 页码：11-22
- 全文大小：549 K
文摘
A multi-variable theta product is examined. It is shown that, under very general choices of the parameters, the quotient of two such general theta products is a root of unity. Special cases are explicitly determined. The second main theorem yields an explicit evaluation of a sum of series of cosines; which greatly generalizes one of Ramanujan's theorems on certain sums of hyperbolic cosines.