Universität zu Köln

Hong, Letong, Mertens, Michael h., Ono, Ken and Zhang, Shengtong (2022). PROOF OF THE ELLIPTIC EXPANSION MOONSHINE CONJECTURE OF CALDARARU, HE, AND HUANG. Proc. Amer. Math. Soc., 150 (12). S. 5047 - 5057. PROVIDENCE: AMER MATHEMATICAL SOC. ISSN 1088-6826

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Abstract

Using predictions in mirror symmetry, Caldararu, He, and Huang recently formulated a Moonshine Conjecture at Landau-Ginzburg points [arXiv:2107.12405, 2021] for Klein's modular j-function at j = 0 and j = 1728. The conjecture asserts that the j-function, when specialized at specific flat coordinates on the moduli spaces of versal deformations of the corresponding CM elliptic curves, yields simple rational functions. We prove this conjecture, and show that these rational functions arise from classical F-2(1)-hypergeometric inversion formulae for the j-function.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Hong, Letong UNSPECIFIED UNSPECIFIED UNSPECIFIED Mertens, Michael h. UNSPECIFIED UNSPECIFIED UNSPECIFIED Ono, Ken UNSPECIFIED UNSPECIFIED UNSPECIFIED Zhang, Shengtong UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-671941
DOI:	10.1090/proc/16032
Journal or Publication Title:	Proc. Amer. Math. Soc.
Volume:	150
Number:	12
Page Range:	S. 5047 - 5057
Date:	2022
Publisher:	AMER MATHEMATICAL SOC
Place of Publication:	PROVIDENCE
ISSN:	1088-6826
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language Mathematics, Applied; Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/67194