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- The '''Riemann zeta function''' is a function very important in about the roots of the zeta function.9 KB (1,547 words) - 02:04, 13 January 2021
- #REDIRECT [[Riemann zeta function]]35 bytes (4 words) - 09:53, 20 February 2016
- #REDIRECT [[Riemann zeta function]]35 bytes (4 words) - 08:16, 19 April 2008
- ...ann zeta function''' is a result due to analytic continuation of [[Riemann zeta function]]: \zeta(s)=2^s\pi^{s-1}\sin\left(\pi s\over2\right)\Gamma(1-s)\zeta(1-s)4 KB (682 words) - 02:56, 13 January 2021
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- ...neq 1</math> for <math>1\le m\le n-1</math>), then <math>\sum_{k=0}^{n-1} \zeta^{km}=
</m ...en the roots of unity can be expressed as <math> 1, \zeta, \zeta^2,\ldots,\zeta^{n-1}</math>.3 KB (558 words) - 20:36, 11 December 2011 - The [[zeta-function]] is a harmonic series when the input is one.2 KB (334 words) - 19:52, 13 March 2022
- ...functional equation]] for the zeta function, it is easy to see that <math>\zeta(s)=0</math> when <math>s=-2,-4,-6,\ldots</math>. These are called the triv ...the [[Möbius function]]. Then one might try to show that <math>\frac{1}{\zeta(s)}</math> admits an [[analytic continuation]] to <math>\Re(s)>\frac{1}{2}<2 KB (425 words) - 02:18, 29 June 2024
- of the zeros of the [[Riemann zeta function]] and the distribution [[Riemann Hypothesis]], namely that the zeta function's nontrivial11 KB (1,749 words) - 21:52, 10 January 2025
- The '''Riemann zeta function''' is a function very important in about the roots of the zeta function.9 KB (1,547 words) - 02:04, 13 January 2021
- ...th>||\epsilon||<math>\varepsilon</math>||\varepsilon||<math>\zeta</math>||\zeta||<math>\eta</math>||\eta16 KB (2,315 words) - 19:35, 4 November 2024
- ...sed for certain types of quantities. <math>z, w, \omega</math> and <math>\zeta</math> are often used as [[complex number|complex]] variables. <math>m</ma1 KB (203 words) - 20:35, 15 November 2007
- | <math>\zeta</math> | Zeta1 KB (216 words) - 09:58, 12 July 2006
- ...ac{1}{1-2} = -1</math>. Analytic continuations are used with the [[Riemann zeta function]], which allows us many interesting results, such as <math>\sum_{n1 KB (180 words) - 19:12, 19 August 2015
- ...^q - 1</math> over the finite field <math>\mathbb{F}_p</math>. Let <math>\zeta</math> be a primitive <math>q</math>th root of unity in <math>K</math>. We <cmath> \tau_q = \sum_{a=0}^{q-1} \genfrac{(}{)}{}{}{a}{q} \zeta^q . </cmath>7 KB (1,182 words) - 15:46, 28 April 2016
- ...at <math>\zeta(2) = \frac{\pi^2}6</math> where <math>\zeta</math> is the [[zeta function]].3 KB (503 words) - 22:28, 1 November 2024
- ...<math>p</math>. This <math>L</math>-function is analogous to the [[Riemann zeta function]] and the Dirichlet <math>L</math>-series that is defined for a bi7 KB (1,102 words) - 16:23, 6 September 2008
- ...triangle). Prove that the area of the quadrilateral <math>\Alpha\Mu\Gamma\Zeta</math> is equal to the area of the triangle <math>\Alpha\Beta\Gamma</math>.791 bytes (117 words) - 13:00, 17 December 2006
- ...triangle). Prove that the area of the quadrilateral <math>\alpha\mu\gamma\zeta</math> is equal to the area of the triangle <math>\alpha\beta\gamma</math>. ...s sides <math>\beta\alpha</math>, <math>\gamma\delta</math> meet at <math>\zeta</math>.2 KB (336 words) - 11:19, 10 October 2007
- Let <math>\omega</math> and <math>\zeta</math> be the two [[complex]] third-roots of 1. Then let ...{2007} + (1 + 1)^{2007} = \sum_{i = 0}^{2007} {2007 \choose i}(\omega^i + \zeta^i + 1)</math>.4 KB (595 words) - 11:14, 25 November 2023
- #REDIRECT [[Riemann zeta function]]35 bytes (4 words) - 09:53, 20 February 2016
- Let <math>\zeta, \xi, \rho</math> be three distinct primitive fifth [[roots of unity]]. Setting <math>x = \zeta, \xi</math>, we have3 KB (572 words) - 16:14, 16 August 2015
- In the more concise cycle notation, we represent a cycle <math>\zeta</math> of order <math>k</math> as <cmath> \begin{pmatrix} x & \zeta(x) & \zeta^2(x) & \cdots & \zeta^{k-1}(x) \end{pmatrix}, </cmath>10 KB (1,668 words) - 14:33, 25 May 2008
- ....2,</math> and <math>\overline {\zeta X} = 21</math>. If <math>\overline {\zeta Z} = \frac {j}{k}</math> where <math>j</math> and <math>k</math> are relati6 KB (909 words) - 06:27, 12 October 2022
- Let the numbers be <math>\eta</math> and <math>\zeta</math>. <cmath>\dfrac{\eta+\zeta}{2}=6\Rightarrow \eta+\zeta=12</cmath>.942 bytes (143 words) - 00:27, 26 June 2016