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Everything about Automorphic form
Type of generalization of periodic functions in Euclidean space
In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group to the complex numbers 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. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Automorphic formA 5-minute orientation
- Skim a recent paper: Automorphic spectra and the conformal bootstrapInfluential work since 2022
- Pick up a classic book: Automorphic Forms and Galois RepresentationsThe most-reprinted book on the subject
- Read the landmark paper: Siegel automorphic form corrections of some Lorentzian Kac-Moody Lie algebrasCited 59 times
- Go sideways: Modular formA closely related topic
- Go sideways: Automorphic functionA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Siegel automorphic form corrections of some Lorentzian Kac-Moody Lie algebras
Rigidity for automorphic forms
Overconvergent algebraic automorphic forms
An $$\widehat{A_4 }$$ extension of ? attached to a non-selfdual automorphic form onGL(3)
On the 4-norm of an automorphic form
Topological automorphic forms
An automorphic form of Ando's theorem
Heterotic sigma models on T 8 and the Borcherds automorphic form Φ12
🆕 Influential since 2022
Automorphic spectra and the conformal bootstrap
Periods of automorphic forms over reductive subgroups
Automorphic Lie Algebras and Modular Forms
Application of automorphic forms to lattice problems
On Fourier coefficients associated to automorphic L-functions over a binary quadratic form and its applications
đź“š Books worth reading
- 📕Automorphic Forms and Galois RepresentationsMinhyong Kim, Fred Diamond · 2014
- 📕Automorphic Forms and l-Functions for the Group GL(n,R)Dorian Goldfeld · 2006
Modern Analysis of Automorphic Forms By ExamplePaul Garrett · 2018
Automorphic Forms, Shimura Varieties and L-FunctionsLaurent Clozel · 1990
Automorphic forms and zeta functionsMasanobu Kaneko, Tomoyoshi Ibukiyama · 2006
Quadratic And Higher Degree FormsKrishnaswami Alladi · 2013- 📕Introductory Lectures on Automorphic FormsWalter L. Baily Jr. · 2015
Families of Automorphic Forms and the Trace FormulaWerner Müller, Sug Woo Shin · 2016
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
- Modular form In number theory and complex analysis, a modular form is a type of function of a complex number variable that possesses a high degree of symmetry, of a…
- Automorphic function 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…
- Cuspidal representation In number theory, cuspidal representations are certain representations of algebraic groups that occur discretely in L2 spaces. The term cuspidal is derived…
- Shimura variety In number theory, a Shimura variety is a higher-dimensional analogue of a modular curve that arises as a quotient variety of a Hermitian symmetric space…
- Selberg trace formula In mathematics, the Selberg trace formula, introduced by Selberg (1956), is an expression for the character of the unitary representation of a Lie group…
- Representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of…
- Arthur–Selberg trace formula In mathematics, the Arthur–Selberg trace formula is a generalization of the Selberg trace formula from the group SL2 to arbitrary reductive groups over…
- Modular curve In number theory and algebraic geometry, a modular curve Y(Γ) is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of…