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Everything about Automorphic function
Mathematical function on a space that is invariant under the action of some group
In mathematics, an automorphic function is a function on a space that is invariant under the action of some group, in other words a function on the quotient space. Often the space is a complex manifold and the group is a discrete group. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Automorphic functionA 5-minute orientation
- Skim a recent paper: Weyl almost automorphic functions and applicationsInfluential work since 2022
- Pick up a classic book: Automorphic Forms and Galois RepresentationsThe most-reprinted book on the subject
- Read the landmark paper: Composition of pseudo almost automorphic and asymptotically almost automorphic functionsCited 132 times
- Go sideways: Automorphic formA closely related topic
- Go sideways: Robert FrickeA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Composition of pseudo almost automorphic and asymptotically almost automorphic functions
Chevalley Groups Over Function Fields and Automorphic Forms
Automorphic period and the central value of Rankin-Selberg L-function
ALMOST AUTOMORPHIC FUNCTIONS
Compact Almost Automorphic Function on Time Scales and Its Application
The symmetric-squareL-function attached to a cuspidal automorphic representation ofGL 3
Models of certain automorphic function fields
III. A memoir on the automorphic linear transformation of a bipartite quadric function
🆕 Influential since 2022
Weyl almost automorphic functions and applications
Complex Creation Operator and Planar Automorphic Functions
Cyclic base change of cuspidal automorphic representations over function fields
Power moments and zero density estimates of automorphic L-function
The 𝕸$_H$(𝘎)-Conjecture and Mazur's conjecture for Abelian Varieties over Global Function Fields (Arithmetic aspects of automorphic forms and automorphic representations)
📚 Books worth reading
- 📕Automorphic Forms and Galois RepresentationsMinhyong Kim, Fred Diamond · 2014
Days with LeninМаксим Горький · 1932
Vorlesungen über die theorie der automorphen functionenFricke, Robert · 1897
Automorphisms of surfaces after Nielsen and ThurstonAndrew J. Casson · 1982- 📕Analytic functions of several complex variablesCarl Ludwig Siegel · 1949
Théorie des fonctions algébriques et de leurs intégralesPaul Appell · 1895
Automorphic Forms, Shimura Varieties and L-FunctionsLaurent Clozel · 1990
Papers on Fuchsian functionsHenri Poincaré · 1985
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Automorphic form 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…
- Robert Fricke Karl Emanuel Robert Fricke (24 September 1861 – 18 July 1930) was a German mathematician, known for his work in complex analysis, especially on elliptic…
- Riemann sphere In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane (also called the closed complex plane): the…
- Schottky group In mathematics, a Schottky group is a special sort of Kleinian group, first studied by Friedrich Schottky (1877). Fix some point p on the Riemann sphere…
- Automorphic factor In mathematics, an automorphic factor is a certain type of analytic function, defined on subgroups of SL(2,R), appearing in the theory of modular forms…
- Harmonic morphism In mathematics, a harmonic morphism is a (smooth) map ϕ : ( M m , g ) → ( N n , h ) {\displaystyle \phi :(M^{m},g)\to (N^{n},h)} between Riemannian manifolds…
- Kleinian group In mathematics, a Kleinian group is a discrete subgroup of the group of orientation-preserving isometries of hyperbolic 3-space H3. The latter, identifiable…
- Felix Klein Felix Christian Klein (/klaɪn/; German: [klaɪn]; 25 April 1849 – 22 June 1925) was a German mathematician, mathematics educator and historian of mathematics…