Introduction to Modular Forms

DOI10.1007/978-1-4939-2830-9_12zbMath1327.11028arXiv1407.1262OpenAlexW1589988510MaRDI QIDQ3460699

Simon C. F. Rose

Publication date: 8 January 2016

Published in: Calabi-Yau Varieties: Arithmetic, Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.1262

zbMATH Keywords

Eisenstein seriesmodular formsFourier coefficientsquasi-modular formsmodular discriminant

Mathematics Subject Classification ID

Fourier coefficients of automorphic forms (11F30) Holomorphic modular forms of integral weight (11F11) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory (11-01)

Uses Software

• ellipticcovers.lib

Cites Work

• Tropical Hurwitz numbers
• A conjectural generating function for numbers of curves on surfaces
• Tropical mirror symmetry for elliptic curves
• BPS states, string duality, and nodal curves on \(K3\)
• The Gross-Kohnen-Zagier theorem in higher dimensions
• Generating functions for the number of curves on abelian surfaces
• Topological strings on elliptic fibrations
• Quantum geometry of elliptic Calabi-Yau manifolds
• Noether-Lefschetz theory and the Yau-Zaslow conjecture
• The enumerative geometry of $K3$ surfaces and modular forms
• Elliptic Calabi–Yau Threefolds over a del Pezzo Surface
• Lectures on Modular Forms. (AM-48)
• BPS states of exceptional non-critical strings
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