Automorphic Forms

In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group G to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup of the topological group. Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups. Modular forms are automorphic forms defined over the groups SL(2, R) or PSL(2, R) with the discrete subgroup being modular group, or one of its congruence subgroups; in this sense the theory of automorphic forms is an extension of the theory of modular forms.
Posts about Automorphic Forms
  • 2015 Breakthrough Prizes Winners Announced

    … of the relation between stability in algebraic geometry and in global differential geometry, both for bundles and for Fano varieties. Maxim Kontsevich, Institut des Hautes Études Scientifiques, for work making a deep impact in a vast variety of mathematical disciplines, including algebraic geometry, deformation theory, symplectic topology, homological…

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