# New pages

From Polymath1Wiki

- 13:42, 12 March 2018 Bounding the derivative of H t - second approach (hist) [12,122 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) [4,448 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) [2,841 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) [28,229 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) [21,530 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) [16,425 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</...")
- 20:32, 14 February 2018 Effective bounds on H t - second approach (hist) [24,017 bytes] Teorth (Talk | contribs) (Created page with "== Heat flow == The functions <math>H_t(z)</math> obey the backwards heat equation <math>\partial_t H_t(z) = -\partial_{zz} H_t(z)</math> with initial condition <math>H_0(z)...")
- 12:32, 12 February 2018 Effective bounds on H t (hist) [20,825 bytes] Teorth (Talk | contribs) (Created page with "== Explicit upper bounds on integrals == We will need effective upper bounds on various integrals that occur as error terms, with explicit constants. Here is a basic tool to...")
- 17:44, 1 February 2018 Asymptotics of H t (hist) [19,883 bytes] Teorth (Talk | contribs) (Created page with "=== Asymptotics for <math>t=0</math> === The approximate functional equation (see e.g. Titchmarsh equation (4.12.4)) asserts that :<math>\displaystyle \zeta(s) = \sum_{n \le...")
- 11:02, 30 January 2018 Dynamics of zeros (hist) [8,099 bytes] Teorth (Talk | contribs) (Created page with "This is a sub-page of page on the De Bruijn-Newman constant, and assumes all the notation from that page. The entire functions <math>H_t(z)</math> obey the backwards heat...")
- 12:50, 25 January 2018 De Bruijn-Newman constant (hist) [11,003 bytes] Teorth (Talk | contribs) (Created page with "For each real number <math>t</math>, define the entire function <math>H_t: {\mathbf C} \to {\mathbf C}</math> by the formula :<math>\displaystyle H_t(z) := \int_0^\infty e^{t...")
- 18:04, 11 January 2018 Intransitive dice (hist) [1,279 bytes] Teorth (Talk | contribs) (Created page with "Gowers' project on intransitive dice. Threads: * [https://gowers.wordpress.com/2017/04/28/a-potential-new-polymath-project-intransitive-dice/ A potential new polymath projec...")
- 14:29, 22 December 2017 Linear norm grant acknowledgments (hist) [1,797 bytes] Teorth (Talk | contribs) (Created page with "Participants should be arranged in alphabetical order of surname. == Participants and contact information == Caution: this list may be incomplete. Participants who have mad...")
- 13:16, 21 December 2017 Linear norm (hist) [10,503 bytes] Teorth (Talk | contribs) (Created page with "This is the wiki page for understanding ''seminorms of linear growth'' on a group <math>G</math> (such as the free group on two generators). These are functions <math>\| \|:...")