Paramodular forms from Calabi-Yau Operators
Nutsa Gegelia, Duco van Straten
TL;DR
This paper explores the conjectural link between Calabi-Yau motives of specific Hodge type and paramodular forms, using computational methods to analyze Euler factors and functional equations.
Contribution
It introduces a method to identify paramodular forms from Calabi-Yau operators and verifies their properties through numerical analysis.
Findings
Identification of potential paramodular forms from Calabi-Yau motives.
Successful computation of Euler factors for selected Calabi-Yau operators.
Numerical validation of the functional equation for primes less than 1000.
Abstract
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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Taxonomy
TopicsAdvanced Algebra and Geometry · Holomorphic and Operator Theory · Mathematical Analysis and Transform Methods