Determinant formulas for multidimensional hypergeometric period matrices

Donald Richards; Qifu Zheng

doi:10.1016/S0196-8858(02)00013-1

Determinant formulas for multidimensional hypergeometric period matrices

Donald Richards, Qifu Zheng

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Abstract

In this article we derive closed-form determinant formulas for certain period matrices whose entries are multidimensional integrals of hypergeometric type with integrands based on power functions. Our results are motivated by the work of Varchenko [Izv. Akad. Nauk SSSR Ser. Mat. 53 (1989) 1206-1235; Izv. Akad. Nauk SSSR Ser. Mat. 54 (1990) 146-158] and Richards and Zheng [Adv. Appl. Math. 28 (2002) 602-633] who derived closed-form expressions for determinants of matrices with entries as multidimensional integrals of rational functions.

Original language	English (US)
Pages (from-to)	137-151
Number of pages	15
Journal	Advances in Applied Mathematics
Volume	29
Issue number	2
DOIs	https://doi.org/10.1016/S0196-8858(02)00013-1
State	Published - Aug 2002

All Science Journal Classification (ASJC) codes

Applied Mathematics

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10.1016/S0196-8858(02)00013-1

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title = "Determinant formulas for multidimensional hypergeometric period matrices",

abstract = "In this article we derive closed-form determinant formulas for certain period matrices whose entries are multidimensional integrals of hypergeometric type with integrands based on power functions. Our results are motivated by the work of Varchenko [Izv. Akad. Nauk SSSR Ser. Mat. 53 (1989) 1206-1235; Izv. Akad. Nauk SSSR Ser. Mat. 54 (1990) 146-158] and Richards and Zheng [Adv. Appl. Math. 28 (2002) 602-633] who derived closed-form expressions for determinants of matrices with entries as multidimensional integrals of rational functions.",

author = "Donald Richards and Qifu Zheng",

note = "Funding Information: * Corresponding author. E-mail address: [email protected] (D. Richards). 1 This research was supported by a grant from the Bell Fund to the Institute for Advanced Study. 2 This research was supported by a grant from the SOSA Fund of the College of New Jersey.",

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T1 - Determinant formulas for multidimensional hypergeometric period matrices

AU - Richards, Donald

AU - Zheng, Qifu

N1 - Funding Information: * Corresponding author. E-mail address: [email protected] (D. Richards). 1 This research was supported by a grant from the Bell Fund to the Institute for Advanced Study. 2 This research was supported by a grant from the SOSA Fund of the College of New Jersey.

PY - 2002/8

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N2 - In this article we derive closed-form determinant formulas for certain period matrices whose entries are multidimensional integrals of hypergeometric type with integrands based on power functions. Our results are motivated by the work of Varchenko [Izv. Akad. Nauk SSSR Ser. Mat. 53 (1989) 1206-1235; Izv. Akad. Nauk SSSR Ser. Mat. 54 (1990) 146-158] and Richards and Zheng [Adv. Appl. Math. 28 (2002) 602-633] who derived closed-form expressions for determinants of matrices with entries as multidimensional integrals of rational functions.

AB - In this article we derive closed-form determinant formulas for certain period matrices whose entries are multidimensional integrals of hypergeometric type with integrands based on power functions. Our results are motivated by the work of Varchenko [Izv. Akad. Nauk SSSR Ser. Mat. 53 (1989) 1206-1235; Izv. Akad. Nauk SSSR Ser. Mat. 54 (1990) 146-158] and Richards and Zheng [Adv. Appl. Math. 28 (2002) 602-633] who derived closed-form expressions for determinants of matrices with entries as multidimensional integrals of rational functions.

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JF - Advances in Applied Mathematics

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ER -

Determinant formulas for multidimensional hypergeometric period matrices

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