In mathematics and theoretical physics, zeta function regularization is a type of regularization or summability method that assigns finite values to divergent...
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1 + 2 + 3 + 4 + ⋯ (redirect from Zeta(-1))
The implementation of this strategy is called zeta function regularization. In zeta function regularization, the series ∑ n = 1 ∞ n {\textstyle \sum _{n=1}^{\infty...
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1 + 1 + 1 + 1 + ⋯ (redirect from Zeta(0))
methods for obtaining values from divergent series, including zeta function regularization. 1 + 1 + 1 + 1 + ⋯ is a divergent series, meaning that its sequence...
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dimensional regularization can be used to study the physics of crystals that macroscopically appear to be fractals. It has been argued that Zeta function regularization...
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The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter ζ (zeta), is a mathematical function of a complex variable defined...
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of regularization procedures include Dimensional regularization Pauli–Villars regularization Lattice regularization Zeta function regularization Causal...
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Divergent series (section Zeta function regularization)
then its value at s = −1 is called the zeta regularized sum of the series a1 + a2 + ... Zeta function regularization is nonlinear. In applications, the numbers...
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Riemann zeta function is a function in complex analysis, which is also important in number theory. It is often denoted ζ ( s ) {\displaystyle \zeta (s)}...
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x^{m-2r}=-{\frac {a^{m-2r+1}}{m-2r+1}}.} Note that this involves (see zeta function regularization) I ( n , Λ ) = ∫ 0 Λ d x x n {\displaystyle I(n,\Lambda )=\int...
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Functional determinant (section Zeta function version)
perform some kind of regularization. The most popular of which for computing functional determinants is the zeta function regularization. For instance, this...
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Renormalization (section Regularization)
inspiration for later attempts at regularization and renormalization in quantum field theory. (See also regularization (physics) for an alternative way...
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In mathematics, the error function (also called the Gauss error function), often denoted by erf, is a function defined as: erf z = 2 π ∫ 0 z e − t 2...
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^{2}}{6\gamma }}\end{aligned}}} also hold true. The digamma function appears in the regularization of divergent integrals ∫ 0 ∞ d x x + a , {\displaystyle...
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regularization is more difficult to use in QCD calculations. P–V serves as a helpful alternative to the more commonly used dimensional regularization...
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Lattice field theory (redirect from Lattice regularization)
regularization Lattice regularization Zeta function regularization Causal perturbation theory Hadamard regularization Point-splitting regularization v...
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mathematics, Hadamard regularization (also called Hadamard finite part or Hadamard's partie finie) is a method of regularizing divergent integrals by...
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practice both numbers are often infinite so are defined using zeta function regularization. It was introduced by Atiyah, Patodi, and Singer (1973, 1975)...
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Roger (1979), "Irrationalité de ζ ( 2 ) {\displaystyle \zeta (2)} et ζ ( 3 ) {\displaystyle \zeta (3)} ", Astérisque, 61: 11–13. Kingdom of Infinite Number:...
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first case, the multiplication is determined with some regularization of generalized function. In the second case, the algebra is constructed as multiplication...
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reference. Quantum triviality Scale invariance Schröder's equation Regularization (physics) Density matrix renormalization group Functional renormalization...
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Renormalization group UV fixed point Causal perturbation theory Zeta function regularization J.D. Bjorken, S. Drell (1965). Relativistic Quantum Fields, Preface...
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Z-transform (section Transfer function)
Probability-generating function Star transform Zak transform Zeta function regularization Mandal, Jyotsna Kumar (2020). "Z-Transform-Based Reversible Encoding"...
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Dirichlet series (category Zeta and L-functions)
_{N}^{\infty }{\frac {S_{f}(y)}{y^{s+1}}}dy.} General Dirichlet series Zeta function regularization Euler product Dirichlet convolution The formulas for both series...
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equivalent to empirical risk minimization with Tikhonov regularization, where in this case the loss function is the hinge loss ℓ ( y , z ) = max ( 0 , 1 − y z...
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where the left-hand side of the equation is the two-point correlation function of the Dirac field. In a new theory, the Dirac field can interact with...
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diagram calculations into the counterterms. When using dimensional regularization, i.e. d 4 p → μ 4 − d d d p {\displaystyle d^{4}p\to \mu ^{4-d}d^{d}p}...
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Bernstein–Sato polynomial (redirect from B-function)
(3): 283–328. MR 0901394. Sato, Mikio; Shintani, Takuro (1972). "On zeta functions associated with prehomogeneous vector spaces". Proceedings of the National...
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gamma function for small arguments. An inequality for Euler's totient function The growth rate of the divisor function In dimensional regularization of Feynman...
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Hilbert–Pólya conjecture (category Zeta and L-functions)
Hilbert–Pólya conjecture states that the non-trivial zeros of the Riemann zeta function correspond to eigenvalues of a self-adjoint operator. It is a possible...
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together with extensions involving non-quadratic regularization functions (e.g., entropic regularization). This combined study gives rise to the "exponential...
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