CM newforms with rational coefficients

DOI10.1007/s11139-008-9147-8zbMath1226.11057arXivmath/0511228OpenAlexW2113467888MaRDI QIDQ1037562

Matthias Schütt

Publication date: 16 November 2009

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0511228

zbMATH Keywords

complex multiplicationHecke characterModular form

Mathematics Subject Classification ID

(K3) surfaces and Enriques surfaces (14J28) Calabi-Yau manifolds (algebro-geometric aspects) (14J32) Fourier coefficients of automorphic forms (11F30) Holomorphic modular forms of integral weight (11F11) Relations with algebraic geometry and topology (11F23)

Related Items (19)

Mahler measure of 3D Landau-Ginzburg potentials ⋮ On the uniqueness of elliptic \(K3\) surfaces with maximal singular fibre ⋮ Newforms with rational coefficients ⋮ Modularity of two double covers of \(\mathbb{P}^5\) branched along 12 hyperplanes ⋮ Solvable lattice sums and quadratic Dirichlet $L$-values ⋮ Three-variable Mahler measures and special values of modular and Dirichlet \(L\)-series ⋮ New realizations of modular forms in Calabi-Yau threefolds arising from \(\phi^{4}\) theory ⋮ Modular forms and \(K3\) surfaces ⋮ Ramanujan type congruences for quotients of Klein forms ⋮ The Manin constant and the modular degree ⋮ A Calabi-Yau threefold coming from two black holes ⋮ A \(K3\) in \(\phi^{4}\) ⋮ \(K3\) mirror symmetry, Legendre family and Deligne's conjecture for the Fermat quartic ⋮ ON MODpREPRESENTATIONS WHICH ARE DEFINED OVER_p: II ⋮ \(K3\) surfaces with non-symplectic automorphisms of 2-power order ⋮ The modularity of \(K3\) surfaces with non-symplectic group actions ⋮ Arithmetic of a singular \(K3\) surface ⋮ Generalised Kummer constructions and Weil restrictions ⋮ On conjectures of Samart

Cites Work

• Modular forms and \(K3\) surfaces
• New examples of threefolds with \(c_ 1=0.\) (With appendix by B. van Geemen)
• Fields of definition of singular \(K3\) surfaces
• Modularity of some non-rigid double octic Calabi-Yau threefolds
• Generalised Kummer constructions and Weil restrictions
• On the modular representations of degree two of \(\text{Gal}({\overline {\mathbb Q}}/{\mathbb Q})\)
• Motivic orthogonal two-dimensional representations of \(\text{Gal}(\overline\mathbb{Q}/\mathbb{Q})\)
• Elliptic fibrations of some extremal \(K3\) surfaces
• Explicit calculation of elliptic fibrations of K3-surfaces and their Belyi-maps
• Higher-Dimensional Modular Calabi–Yau Manifolds
• Imaginary quadratic fields with class group exponent 5
• INTEGRAL SYMMETRIC BILINEAR FORMS AND SOME OF THEIR APPLICATIONS
• Exponents of the class groups of complex quadratic fields
• On the Exponent of the Ideal Class Groups of Complex Quadratic Fields
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