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...e of [[zeta function]] introduced by [[Kohji Matsumoto]] in 1990. They are functions of the form where ''p'' is a [[Prime number|prime]] and ''A''_''p'' is a [[polynomial]]. ...

{{for|the Shintani zeta function of a vector space|Prehomogeneous vector space}} ...Shintani|year=1976}}. They include [[Hurwitz zeta function]]s and [[Barnes zeta function]]s. ...

...he '''Arakawa–Kaneko zeta function''' is a generalisation of the [[Riemann zeta function]] which generates special values of the [[polylogarithm]] function The zeta function <math>\xi_k(s)</math> is defined by ...

In [[mathematics]], the '''Ruelle zeta function''' is a [[zeta function]] associated with a [[dynamical system]]. It is named after mathe ...ion on ''M'' with values in ''d''&nbsp;×&nbsp;''d'' complex matrices. The zeta function of the first kind is<ref name=T28>Terras (2010) p.&nbsp;28</ref> ...

...ine the [[Hardy space]] ''H''²(∂&Omega;) to be the closure in ''L''²(∂&Omega;) of the restrictions of elements of ''A''(&Omega;) t :<math>Pf(z) = \int_{\partial\Omega} f(\zeta)\overline{k_z(\zeta)}\,d\sigma(\zeta).</math> ...

...|Crandall|1996}}, is a function analogous to the [[Riemann zeta function]] and related to the zeros of the [[Airy function]]. [[File:Airy Functions.svg|thumb|The Airy functions Ai and Bi]] ...

The '''[[zeta function (disambiguation)|zeta function]] of a mathematical [[operator (mathematics)|operator]]''' <math>\ for those values of ''s'' where this expression exists, and as an [[analytic continuation]] of this function for other values of ''s''. ...

It is named after William Feller (1906–1970) and Erhard Tornier (1894–1982)<ref>{{cite web|url=http://oeis.org/wiki/Feller–T & = {1\over2}\left(1+{{1}\over{\zeta(2)}} \prod_{n=1}^\infty \left( 1-{{1}\over{p_n^2 -1}} \right) \right) \\[4p ...

.... W. |last=Barnes|year=1901}}. It is further generalized by the [[Shintani zeta function]]. The Barnes zeta function is defined by ...

...ning the distances between zeros and the density of zeros of the [[Riemann zeta function]]. ...Sci.| volume=158| year=1914}}</ref> that the Riemann zeta function <math>\zeta\bigl(\tfrac{1}{2}+it\bigr)</math> has infinitely many real zeros. ...

...long with a form of the [[orthogonal projection]] from <math>\left.\right. L^2 </math> to <math>\left.\right. H_2 </math>. }}</ref> contains the following theorem presented also in [[Joseph L. Walsh]]'s well-known monograph ...

...a [[theorem]] about the density of zeros of the [[Riemann zeta function]] &zeta;(1/2&nbsp;+&nbsp;''it''). It is known that the function has infinitely many ...ittlewood zeta function conjectures|Hardy–Littlewood conjecture '''2''']]; and he proved that for any ...

.../euclid.cmp/1104248198 }}</ref> Note that in,<ref name=":0" /> Witten zeta functions do not appear as explicit objects in their own right. If <math>G</math> is a compact semisimple Lie group, the associated Witten zeta function is (the meromorphic continuation of) the series ...

...1=Lehman| first1=R. S. | title=On the Distribution of Zeros of the Riemann Zeta-Function | doi=10.1112/plms/s3-20.2.303| year=1970| journal=Proceedings of ...list of Gram points <math> \{g_i \mid 0\leqslant i \leqslant m \} </math> and a complementary list <math> \{h_i \mid 0\leqslant i \leqslant m \} </math>, ...

Taking the real and imaginary parts of the logarithm, this implies the two inequalities and ...

In [[algebraic geometry]], the '''motivic zeta function''' of a [[smooth algebraic variety]] <math>X</math> is the [[forma ...math>X^n</math> by the action of the [[symmetric group]] <math>S_n</math>, and <math>[X^{(n)}]</math> is the class of <math>X^{(n)}</math> in the ring of ...

...wn by 1, interpolates the factorial and extends it to [[real number|real]] and [[complex number]]s in a different way than Euler's gamma function. It is d where <math>\Phi</math> is the [[Lerch zeta function]], and as ...

...vii and ix.</ref><ref>Pemantle and Wilson 2013, pp. xi.</ref><ref>Flajolet and Sedgewick 2009, pp. ix.</ref> ...d later the [[Hardy–Littlewood circle method|circle method]].<ref>Pemantle and Wilson 2013, pp. 62.</ref> ...

...av V.|title= Three notes on Ser's and Hasse's representations for the zeta-functions |journal= INTEGERS: The Electronic Journal of Combinatorial Number Theory | and may also use a different notation for them (the most used alternative notat ...

...d it from the '''Riemann–Siegel integral formula''', an expression for the zeta function involving [[contour integral]]s. It is often used to compute value If ''M'' and ''N'' are non-negative integers, then the zeta function is equal to ...