The \(L\)-series of certain rigid Calabi-Yau threefolds

DOI10.1006/jnth.1999.2449zbMath0971.14034OpenAlexW2061515989MaRDI QIDQ1976811

Helena A. Verrill

Publication date: 4 July 2001

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.1999.2449

zbMATH Keywords

toric varietyCalabi-Yau threefoldWeyl chambersroot latticeL-series

Mathematics Subject Classification ID

Calabi-Yau manifolds (algebro-geometric aspects) (14J32) (3)-folds (14J30) Structure of families (Picard-Lefschetz, monodromy, etc.) (14D05) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Families, moduli, classification: algebraic theory (14J10) Dedekind eta function, Dedekind sums (11F20) Transcendence (general theory) (11J81) Relations with algebraic geometry and topology (11F23)

Related Items

CONGRUENCES RELATED TO MODULAR FORMS, MODULAR CALABI–YAU THREEFOLDS OF LEVEL EIGHT, The Langlands program and string modular \(K3\) surfaces, Modularity of a certain Calabi-Yau threefold and combinatorial congruences, Lifting cusp forms to Maass forms with an application to partitions, Hessian \(K3\) surfaces of non-Sylvester type, The Mahler measure for \(K3\) hypersurfaces, The geometry of the third moment of exponential sums, The points of a certain fivefold over finite fields and the twelfth power of the eta function, Diophantine triples and \(K3\) surfaces

Cites Work

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• On the Picard-Fuchs equation and the formal Brauer group of certain elliptic \(K3\)-surfaces
• The modularity conjecture for rigid Calabi-Yau threefolds over \(\mathbb{Q}\)
• Another congruence for the Apéry numbers
• On the geometry and arithmetic of some Siegel modular threefolds
• Modularity of a certain Calabi-Yau threefold
• Root lattices and pencils of varieties
• CONGRUENCES RELATED TO MODULAR FORMS
• Monodromy and Picard-Fuchs equations for families of $K3$-surfaces and elliptic curves
• Formal Groups and Congruences for L-Functions
• Monstrous Moonshine
• Birational Calabi--Yau n-folds have equal Betti numbers
• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties