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Everything about Modular group
Orientation-preserving mapping class group of the torus
In mathematics, the modular group is the projective special linear group of matrices with integer coefficients and determinant, such that the matrices and are identified. The modular group acts on the upper-half of the complex plane by linear fractional transformations. The name "modular group" comes from the relation to moduli spaces, and not from modular arithmetic. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Modular groupA 5-minute orientation
- Skim a recent paper: Phase II Randomized Trial of Transoral Surgery and Low-Dose Intensity Modulated Radiation Therapy in Resectable p16+ Locally Advanced Oropharynx Cancer: An ECOG-ACRIN Cancer Research Group Trial (E3311)Influential work since 2022
- Pick up a classic book: Moonshine beyond the MonsterThe most-reprinted book on the subject
- Read the landmark paper: Discrete Heisenberg-Weyl Group and modular groupCited 229 times
- Go sideways: Modular curveA closely related topic
- Go sideways: SL2(R)A closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Discrete Heisenberg-Weyl Group and modular group
Finite group modular data
On Siegel's modular group
Modular invariants for group-theoretical modular data. I
Hermitian Modular Functions. III: The Hermitian Modular Group
Subgroups of the Classical Modular Group
On Ihara's modular group
Isomorphism of modular group algebras
🆕 Influential since 2022
Phase II Randomized Trial of Transoral Surgery and Low-Dose Intensity Modulated Radiation Therapy in Resectable p16+ Locally Advanced Oropharynx Cancer: An ECOG-ACRIN Cancer Research Group Trial (E3311)
Minimal seesaw and leptogenesis with the smallest modular finite group
Modular Generation of (Iodinated) Polyarenes Using Triethylgermane as Orthogonal Masking Group
Modular curves, the Tate-Shafarevich group and Gopakumar-Vafa invariants with discrete charges
Modular synthesis of triazoles from 2-azidoacrylamides having a nucleophilic amino group
📚 Books worth reading
Moonshine beyond the MonsterTerry Gannon · 2006
Representation theory of finite groups and associative algebrasCharles W. Curtis · 1962
Local Representation TheoryJ. L. Alperin · 1986
Modular Representations of Finite Groups of Lie TypeJames E. Humphreys · 2005
On central critical values of the degree four L-functions for GSp(4)Masaaki Furusawa, Joseph A. Shalika · 2003
Elementi della teoria delle funzioni poliedriche e modulariG. Vivanti · 1906
Introductory lectures on Siegel modular formsHelmut Klingen · 2008
Modular Representation Theory of Finite GroupsPeter Schneider · 2012
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- 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…
- SL2(R) In mathematics, the special linear group SL(2, R) or SL2(R) is the group of 2 × 2 real matrices with determinant one: SL ( 2 , R ) = { ( a b c d ) : a…
- PSL(2,7) In mathematics, the projective special linear group PSL(2, 7), isomorphic to GL(3, 2), is a finite simple group that has important applications in algebra…
- Fuchsian group In mathematics, a Fuchsian group is a discrete subgroup of PSL(2,R). The group PSL(2,R) can be regarded equivalently as a group of orientation-preserving…
- Möbius transformation In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form f(z)=az+bcz+d of one complex variable…
- 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…
- Poincaré half-plane model In non-Euclidean geometry, the Poincaré half-plane model is a way of representing the hyperbolic plane using points in the familiar Euclidean plane. Specificall…
- Congruence subgroup In mathematics, a congruence subgroup of a matrix group with integer entries is a subgroup defined by congruence conditions on the entries. A very simple…