A finite spectral representation of the partition function

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• 作者：Michael Weba
• 关键词：Finite representations of the partition function ; Finite representations of the divisor function ; Upper Hessenberg matrix ; Spectral representation ; Matrix function
• 刊名：The Ramanujan Journal
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：42
• 期：1
• 页码：29-42
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Number Theory; Field Theory and Polynomials; Combinatorics; Fourier Analysis; Functions of a Complex Variable;
• 出版者：Springer US
• ISSN：1572-9303
• 卷排序：42

文摘

Finite representations of the partition function in terms of powers and eigenvalues of a sparse upper Hessenberg matrix are established. The trace of this matrix also yields finite representations of the divisor function. Several identities between partition numbers and other quantities such as matrix functions are derived.