In mathematics, the Witten zeta function, is a function associated to a root system that encodes the degrees of the irreducible representations of the...

zeta function of a Riemann surface Shimizu L-function Shintani zeta function Subgroup zeta function Witten zeta function of a Lie group Zeta function...

dx} when n = 1 , 2 {\displaystyle n=1,2} in terms of the Tornheim–Witten zeta function and its derivatives. In addition, it is also known that lim n → ∞...

non-negative coefficients. Witten zeta functions are however not special cases of Shintani zeta functions because in Witten zeta functions the linear forms are...

Edward Witten (born August 26, 1951) is an American theoretical physicist known for his contributions to string theory, topological quantum field theory...

to special values of the Riemann zeta function. Zagier found a formula for the value of the Dedekind zeta function of an arbitrary number field at s = 2...

\zeta (s)=\sum _{n=1}^{\infty }n^{-s}={\frac {1}{1^{s}}}+{\frac {1}{2^{s}}}+{\frac {1}{3^{s}}}+\cdots } The Riemann zeta function ζ(s) is a function whose...

number theory. The conjectures concern the generating functions (known as local zeta functions) derived from counting points on algebraic varieties over...

 291–400. doi:10.1002/9780470116449.ch6. ISBN 9780470116449. James, Gareth; Witten, Daniela; Hastie, Trevor; Tibshirani, Robert (2013). "Support Vector Machines"...

application of topological recursion was to Gromov–Witten invariants. Marino and BKMP conjectured that Gromov–Witten invariants of a toric Calabi–Yau 3-fold X...

group of the ring of integers of a number field to the field's Dedekind zeta function. Bombieri–Lang conjectures on densities of rational points of algebraic...

∞ Q i j ζ j d ζ {\displaystyle \Omega _{k}=d(\zeta ^{-k})+\sum _{j=1}^{\infty }Q_{ij}\zeta ^{j}d\zeta } . Ω k {\displaystyle \Omega _{k}} is normalized...

partition function of the noise in terms of the dynamical variables of the model using BRST gauge-fixing procedure. The resulting expression is the Witten index...

ξ d η . {\displaystyle d\zeta \wedge d{\bar {\zeta }}=(d\xi +id\eta )\wedge (d\xi -id\eta )=-2id\xi d\eta .} If a function M ( z ) {\displaystyle M(z)}...

medal as of 2022. With the exception of two PhD holders in physics (Edward Witten and Martin Hairer), only people with a PhD in mathematics have won the medal...

eigenvalues on k-forms are λj then the zeta function ζk is defined to be ζ k ( s ) = ∑ λ j > 0 λ j − s {\displaystyle \zeta _{k}(s)=\sum _{\lambda _{j}>0}\lambda...

include number theory, zeta theory, and mathematical analysis. He is mostly recognized for the Matsumoto zeta function, a zeta function named after him. He...

\rho ={\frac {1}{2}}(\zeta _{1}\wedge \zeta _{2}\wedge \zeta _{3}+{\bar {\zeta _{1}}}\wedge {\bar {\zeta _{2}}}\wedge {\bar {\zeta _{3}}})} where ζ 1 =...

{\displaystyle \operatorname {sgn}(x)} is the sign function. Other regulators, such as the zeta function regulator, may be used. The need for both a positive...

Courrier 41(7) (2001). Full text available at : I.O.P Magazines. E. Elizalde; Zeta regularization techniques with Applications. N. N. Bogoliubov, D. V. Shirkov...

\end{aligned}}} where ζ {\displaystyle \zeta } is the Riemann zeta function, and ζ ′ ( − 1 ) = − 0.1654211437 {\displaystyle \zeta '(-1)=-0.1654211437} . This allows...

Michael Rossmann Royer oscillator – George H. Royer Ruelle operator, zeta function – David Ruelle Ruelle–Perron–Frobenius theorem – David Ruelle, Oskar...

large-frequency excitations corresponding to analytic continuation of the Riemann zeta function to s = 0 is assumed to make sense physically in some way, then one has...

) ) {\displaystyle \Pi \lambda =\exp(-\zeta '(0))} where ζ ( s ) {\displaystyle \zeta (s)} is the zeta function operator of the Laplacian D t ∗ D t {\displaystyle...

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

conjecture about the zeros of the zeta function. The primes 2, 3, 5, 7, 11, 13, 17, 19,... are described by the Riemann zeta function, and Dyson had previously...

_{\mu }+\zeta m\omega K\right)=-\left(\partial _{t}^{2}-{\vec {\nabla }}\cdot {\vec {\nabla }}+\eta \zeta ^{*}m^{2}\right)=-\left(\square +\eta \zeta ^{*}m^{2}\right)}...

121q1604S. doi:10.1103/PhysRevLett.121.171604. PMID 30411950. S2CID 53237231. Witten, Edward. "Spacetime reconstruction". Sleight, Charlotte; Taronna, Massimo...

Raoult Riemann zeta function Riemann hypothesis Riemann integral Riemann lemma Riemannian manifold Riemann sphere Riemann theta function  See also: List...

118–144. doi:10.1016/0550-3213(74)90010-8. Green, M.B.; Schwarz, J.H.; Witten, E. (2012). "4". Superstring Theory: 25th Anniversary Edition: Volume 1...