Live briefing
Everything about Liouville function
Arithmetic function
In number theory, the Liouville function, named after French mathematician Joseph Liouville and denoted, is an important arithmetic function. Its value is if is the product of an even number of prime numbers, and if it is the product of an odd number of prime numbers. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Liouville functionA 5-minute orientation
- Skim a recent paper: The two-sphere partition function from timelike Liouville theory at three-loop orderInfluential work since 2022
- Pick up a classic book: Sturm-Liouville Theory and its ApplicationsThe most-reprinted book on the subject
- Read the landmark paper: On the Liouville three-point functionCited 195 times
- Go sideways: Grunsky matrixA closely related topic
- Go sideways: Stochastic portfolio theoryA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
On the Liouville three-point function
Boundary Liouville field theory: boundary three-point function
Wigner function in Liouville space: A canonical formalism
Three-point function in the minimal Liouville gravity
Sturm-Liouville operators with an indefinite weight function
Three-point function in the minimal Liouville gravity
Sturm-Liouville Eigenvalues via a Phase Function
Discrete Sturm-Liouville operators and some problems of function theory
🆕 Influential since 2022
The two-sphere partition function from timelike Liouville theory at three-loop order
Deriving weighted Newton-type inequalities for diverse function classes through Riemann–Liouville fractional integrals
Differential sandwich theorems involving Riemann-Liouville fractional integral of $ q $-hypergeometric function
Sandwich-type results regarding Riemann-Liouville fractional integral of q-hypergeometric function
Is the Moyal equation for the Wigner function a quantum analogue of the Liouville equation?
📚 Books worth reading
Sturm-Liouville Theory and its ApplicationsMohammed Abdelrahman Al-Gwaiz · 2007
Applied Pseudoanalytic Function TheoryVladislav V. Kravchenko · 2009
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Grunsky matrix In complex analysis and geometric function theory, the Grunsky matrices, or Grunsky operators, are infinite matrices introduced in 1939 by Helmut Grunsky…
- Stochastic portfolio theory Stochastic portfolio theory (SPT) is a mathematical theory for analyzing stock market structure and portfolio behavior introduced by E. Robert Fernholz…
- Lambert series In mathematics, a Lambert series, named for Johann Heinrich Lambert, is a series taking the form S ( q ) = ∑ n = 1 ∞ a n q n 1 − q n . {\displaystyle S(q)=\sum…
- Vaughan's identity In mathematics and analytic number theory, Vaughan's identity is an identity found by R. C. Vaughan (1977) that can be used to simplify Vinogradov's work…
- Marcum Q-function In statistics, the generalized Marcum Q-function of order ν {\displaystyle \nu } is defined as Q ν ( a , b ) = 1 a ν − 1 ∫ b ∞ x ν exp ( − x 2 + a 2…
- Multiple zeta function In mathematics, the multiple zeta functions are generalizations of the Riemann zeta function, defined by ζ ( s 1 , … , s k ) = ∑ n 1 > n 2 > ⋯ > n k >…
- Riesz mean In mathematics, the Riesz mean is a certain mean of the terms in a series. They were introduced by Marcel Riesz in 1911 as an improvement over the Cesàro…
- Smooth maximum In mathematics, a smooth maximum of an indexed family x1, ..., xn of numbers is a smooth approximation to the maximum function max ( x 1 , … , x n ) ,…