A finite field hypergeometric function associated to eigenvalues of a Siegel eigenform

DOI10.1142/S1793042115501134zbMATH Open1395.11078arXiv1205.1006OpenAlexW1819147413WikidataQ60118090 ScholiaQ60118090MaRDI QIDQ3458269

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Publication date: 18 December 2015

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Abstract: Although links between values of finite field hypergeometric functions and eigenvalues of elliptic modular forms are well known, we establish in this paper that there are also connections to eigenvalues of Siegel modular forms of higher degree. Specifically, we relate the eigenvalue of the Hecke operator of index $p$ of a Siegel eigenform of degree 2 and level 8 to a special value of a ${}_4{F}_3$-hypergeometric function.

Full work available at URL: https://arxiv.org/abs/1205.1006

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