# New pages

From Polymath1Wiki

- 16:57, 12 June 2018 Coloring R 2 (hist) [24,686 bytes] Teorth (Talk | contribs) (Created page with "Let <math>R_1 = {\bf Z}[\omega]</math> denote the Eisenstein integers, where <math>\omega := e^{2\pi i/3}</math>, thus <math>\omega+\omega^2+1=0</math>. The quotient <math>R_...")
- 10:57, 10 May 2018 Excluding bichromatic vertices (hist) [10,253 bytes] Teorth (Talk | contribs) (Created page with " Category:Polymath16")
- 03:36, 7 May 2018 Algebraic formulation of Hadwiger-Nelson problem (hist) [19,919 bytes] Pgibbs (Talk | contribs) (Created page with "''This is a part of Polymath16 - for the main page, see Hadwiger-Nelson problem.''")
- 10:27, 3 May 2018 Probabilistic formulation of Hadwiger-Nelson problem (hist) [40,798 bytes] Teorth (Talk | contribs) (Created page with "Suppose that we have a 4-coloring <math>c: {\bf C} \to \{1,2,3,4\}</math> of the complex plane with no unit edges monochromatic, thus :<math>c(z) \neq c(w) \hbox{ whenever }...")
- 13:21, 13 April 2018 Hadwiger-Nelson problem (hist) [39,364 bytes] Teorth (Talk | contribs) (Created page with "The Chromatic Number of the Plane (CNP) is the chromatic number of the graph whose vertices are elements of the plane, and two points are connected by an edge if they are a un...")
- 10:28, 29 March 2018 Zero-free regions (hist) [10,474 bytes] Teorth (Talk | contribs) (Created page with "The table below lists various regions of the <math>(t,y,x)</math> parameter space where <math>H_t(x+iy)</math> is known to be non-zero. In some cases the parameter :<math> N...")
- 18:20, 23 March 2018 Bounding the derivative of H t - third approach (hist) [7,109 bytes] Teorth (Talk | contribs) (Created page with "To compute <math>H_t(x+iy)</math>, we begin with the heat fundamental solution formula :<math> H_t(x+iy) = \frac{1}{8} \int_{-\infty}^\infty \xi( \frac{1-y+ix}{2} + \sqrt{t}...")
- 13:42, 12 March 2018 Bounding the derivative of H t - second approach (hist) [12,149 bytes] Teorth (Talk | contribs) (Created page with "We have :<math>H_t(z) = \frac{1}{2} \int_{\bf R} e^{tu^2} \Phi(u) e^{izu}\ du</math> and hence on differentiation under the integral sign :<math>H'_t(z) = \frac{i}{2} \int_...")
- 01:15, 10 March 2018 Riemann-Siegel formula (hist) [4,765 bytes] Teorth (Talk | contribs) (Created page with "'''Lemma 1''' For any complex number <math>z</math>, one has :<math> \int_{0 \uprightarrow 1} \frac{e^{i\pi u^2} + 2\pi i z u}}{e^{i\pi u} - e^{-i\pi u}}\ du = \frac{e^{i\pi z...")
- 21:22, 8 March 2018 Bounding the derivative of H t (hist) [4,473 bytes] Teorth (Talk | contribs) (Created page with "We continue using the notation from Effective bounds on H_t - second approach. Since :<math>H_t(z) = \frac{1}{8} \xi_t( s) </math> with <math>s := \frac{1+iz}{2}</math>,...")
- 16:41, 4 March 2018 Estimating a sum (hist) [7,429 bytes] Teorth (Talk | contribs) (Created page with "For any <math>\sigma, t>0</math> and natural number <math>N</math>, introduce the sum :<math>F_{\sigma,t}(N) := \sum_{n=1}^N \frac{1}{n^{\sigma + \frac{t}{4} \log\frac{N^2}{n...")
- 17:49, 1 March 2018 Controlling H t-A-B/B 0 (hist) [28,254 bytes] Teorth (Talk | contribs) (Created page with " As computed in Effective bounds on H_t - second approach, there is an effective bound :<math>|H_{eff} - A^{eff} - B^{eff}| \leq E_1 + E_2 + E_3</math> where :<math>H_{0,1...")
- 17:48, 1 March 2018 Controlling A+B/B 0 (hist) [21,641 bytes] Teorth (Talk | contribs) (Created page with " Some numerical data on <math>|A+B/B_0|</math> [https://terrytao.wordpress.com/2018/02/02/polymath15-second-thread-generalising-the-riemann-siegel-approximate-functional-equat...")
- 10:39, 23 February 2018 Polymath15 test problem (hist) [17,848 bytes] Teorth (Talk | contribs) (Created page with "We are initially focusing attention on the following :'''Test problem''' For <math>t=y=0.4</math>, can one prove that <math>H_t(x+iy) \neq 0</math> for all <math>x \geq 0</...")