Paramodular forms from Calabi-Yau Operators

Duco van Straten; Nutsa Gegelia

Paramodular forms from Calabi-Yau Operators

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arxiv 2408.10183 v1 pith:KUWOGYD3 submitted 2024-08-19 math.NT math.AG

Nutsa Gegelia , Duco van Straten This is my paper · ORCID

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keywords calabi-yaueulerformsmethodoperatorsparamodularaeszapproximate

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In this note we report on the conjectural identification of paramodular forms from Calabi-Yau motives of Hodge type (1, 1, 1, 1) of moderately low conductor. We calculate Euler factors from Calabi-Yau operators from the AESZ database by the method described in P. Candelas, X. dela Ossa and D. van Straten, seek a fit with the tables provided by E. Assaf, W. Ladd, G. Rama, G. Tornaria, and J. Voight and for consistency check the approximate functional equation for the Euler product for primes < 1000 numerically, using the PARI implementation of T. Dokchitser's method.

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Residual paramodularity of a certain Calabi-Yau threefold
math.NT 2024-12 conditional novelty 7.0 of 10

The mod-5 representation on H^3 of the Calabi-Yau threefold Y79 is shown to be isomorphic to the mod-5 residual representation of the paramodular form F79.

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