Modularity of a certain Calabi-Yau threefold

Scott Ahlgren; Ken Ono

doi:10.1007/s006050050069

Modularity of a certain Calabi-Yau threefold

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Abstract

The Langlands program predicts that certain Calabi-Yau threefolds are modular in the sense that their L-series correspond to the Mellin transforms of weight 4 newforms. Here we prove that the L-function of the threefold given by ∑⁴_i=1 (x_i + x^-1_i) = 0 is η⁴(2z)η⁴(4z), the unique normalized eigenform in S₄(Γ₀(8)).

Original language	English (US)
Pages (from-to)	129-177
Number of pages	49
Journal	Monatshefte fur Mathematik
Volume	129
Issue number	3
DOIs	https://doi.org/10.1007/s006050050069
State	Published - 2000
Externally published	Yes

Keywords

Calabi-yau threefold
Modular forms
Trace formula

ASJC Scopus subject areas

General Mathematics

Online availability

10.1007/s006050050069

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KW - Trace formula

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Modularity of a certain Calabi-Yau threefold

Abstract

Keywords

ASJC Scopus subject areas

Online availability

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