In mathematics and theoretical physics, zeta function regularization is a type of regularization or summability method that assigns finite values to divergent...

The implementation of this strategy is called zeta function regularization. In zeta function regularization, the series ∑ n = 1 ∞ n {\textstyle \sum _{n=1}^{\infty...

methods for obtaining values from divergent series, including zeta function regularization. 1 + 1 + 1 + 1 + ⋯ is a divergent series, meaning that its sequence...

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...

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...

of regularization procedures include Dimensional regularization Pauli–Villars regularization Lattice regularization Zeta function regularization Causal...

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...

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)}...

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...

perform some kind of regularization. The most popular of which for computing functional determinants is the zeta function regularization. For instance, this...

inspiration for later attempts at regularization and renormalization in quantum field theory. (See also regularization (physics) for an alternative way...

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...

regularization is more difficult to use in QCD calculations. P–V serves as a helpful alternative to the more commonly used dimensional regularization...

^{2}}{6\gamma }}\end{aligned}}} also hold true. The digamma function appears in the regularization of divergent integrals ∫ 0 ∞ d x x + a , {\displaystyle...

mathematics, Hadamard regularization (also called Hadamard finite part or Hadamard's partie finie) is a method of regularizing divergent integrals by...

practice both numbers are often infinite so are defined using zeta function regularization. It was introduced by Atiyah, Patodi, and Singer (1973, 1975)...

regularization Lattice regularization Zeta function regularization Causal perturbation theory Hadamard regularization Point-splitting regularization v...

Renormalization group UV fixed point Causal perturbation theory Zeta function regularization J.D. Bjorken, S. Drell (1965). Relativistic Quantum Fields, Preface...

Roger (1979), "Irrationalité de ζ ( 2 ) {\displaystyle \zeta (2)} et ζ ( 3 ) {\displaystyle \zeta (3)} ", Astérisque, 61: 11–13. Kingdom of Infinite Number:...

first case, the multiplication is determined with some regularization of generalized function. In the second case, the algebra is constructed as multiplication...

reference. Quantum triviality Scale invariance Schröder's equation Regularization (physics) Density matrix renormalization group Functional renormalization...

Probability-generating function Star transform Zak transform Zeta function regularization Mandal, Jyotsna Kumar (2020). "Z-Transform-Based Reversible Encoding"...

_{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...

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...

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...

(3): 283–328. MR 0901394. Sato, Mikio; Shintani, Takuro (1972). "On zeta functions associated with prehomogeneous vector spaces". Proceedings of the National...

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...

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}...

gamma function for small arguments. An inequality for Euler's totient function The growth rate of the divisor function In dimensional regularization of Feynman...

field theory String cosmology Supergravity The Elegant Universe Zeta function regularization Sen, Ashoke (1999-12-29). "Universality of the tachyon potential"...