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	ABOUT: [Introduction][History][Related areas][Subfields] POINTERS: [Texts][Software][Web links][Selected topics here] 11F: Discontinuous groups and automorphic forms

Introduction

History

Applications and related fields

Subfields

• 11F03: Modular and automorphic functions
• 11F06: Structure of modular groups and generalizations; arithmetic groups [See also 20H05, 20H10, 22E40]
• 11F11: Modular forms, one variable
• 11F12: Automorphic forms, one variable
• 11F20: Dedekind eta function, Dedekind sums
• 11F22: Relationship to Lie algebras and finite simple groups
• 11F23: Relations with algebraic geometry and topology [new in 2000]
• 11F25: Hecke-Petersson operators, differential operators (one variable)
• 11F27: Theta series; Weil representation
• 11F30: Fourier coefficients of automorphic forms
• 11F32: Modular correspondences, etc.
• 11F33: Congruences for modular and p-adic modular forms [See also 14G20, 22E50]
• 11F37: Forms of half-integer weight; nonholomorphic modular forms
• 11F41: Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20]
• 11F46: Siegel modular groups and their modular and automorphic forms
• 11F50: Jacobi forms [new in 2000]
• 11F52: Modular forms associated to Drinfel´ d modules [new in 2000]
• 11F55: Other groups and their modular and automorphic forms (several variables)
• 11F60: Hecke-Petersson operators, differential operators (several variables)
• 11F66: Dirichlet series and functional equations in connection with modular forms
• 11F67: Special values of automorphic L-series, periods of modular forms, cohomology, modular symbols
• 11F70: Representation-theoretic methods; automorphic representations over local and global fields
• 11F72: Spectral theory; Selberg trace formula
• 11F75: Cohomology of arithmetic groups
• 11F80: Galois properties
• 11F85: p-adic theory, local fields [See also 14G20, 22E50]
• 11F99: None of the above, but in this section

Parent field: 11: Number Theory

Browse all (old) classifications for this area at the AMS.

Textbooks, reference works, and tutorials

• Shimura, Goro: "Introduction to the arithmetic theory of automorphic functions", Publications of the Mathematical Society of Japan, 11. Princeton University Press, Princeton, NJ, 1994. 271 pp. ISBN 0-691-08092-5
• Apostol, Tom M.: "Modular functions and Dirichlet series in number theory", Springer-Verlag, New York-Berlin, 1990. 204 pp. ISBN 0-387-97127-0

Software and tables

Other web sites with this focus

Selected topics at this site

• A tour of moduli spaces, stacks, PSL(2,Z), and related delights. [John Baez]
• Theta functions: Sum(x^(n^2)), Jacobi identity, use to solve polynomial equations;
• Theta functions ( Sum a^k^2, k from 0 to n) and the Jacobi identity.
• Theta-functions (e.g. theta(z) = sum(exp q^(n^2) )
• Dirichlet series related to zeta function and arithmetic functions
• Recursive formula for the Ramanujan Tau function