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...

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...

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...

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...

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

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)}...

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

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...

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

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...

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

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

^{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...

In mathematics, the error function (also called the Gauss error function), often denoted by erf, is a function e r f : C → C {\displaystyle \mathrm {erf}...

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

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"...

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

_{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...

zeta function*, where it is the first of the Stieltjes constants. Values of the derivative of the Riemann zeta function and Dirichlet beta function.: 137 ...

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

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...

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}...

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...

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