07 Vilmos Totik Erdős on polynomials And Ben Green The sum-free set constant is ⅓ 1:45:31 Tomasz Łuczak Threshold functions a historical overview 54:37 Timothy Gowers Erdős and arithmetic progressions 52:06 Zoltan Szabo Heegaard Floer theory an introduction vol2 1:03:24 zoltan szabo...
Timothy Browning When is a random Diophantine equation soluble over [.] (NTWS 1 52:31 Thomas Gauthier A complex analytic approach to sparsity, rigidity and uniformity 55:59 Terence Tao Infinite Partial Sumsets in the Primes (NTWS 160) 43:50 Solymosi_Recording 44:38 Siksek_Recording 57...
The function where is the Riemann function has a Fourier representation where is the super-exponentially decaying function The Riemann hypothesis is equivalent to the claim that all the zeroes of are real. De Bruijn introduced (in different notation) the deformations of ; one can view this as ...
From a statistical point of view, this is an outlier with a very low probability, so much so that even the least superstitious people can't help but feel moved: is this the kind of price that God has already secretly labeled? Simmons once said to a friend, “I've either gotten A or...
Where does the gamma function come from? What is the fundamental period of a function that is the sum of two-period functions? How to express a function as the composition of spherical harmonics? What is the harmonic mean formula? What are one-to-one and onto functions? Explain with exampl...
Our starting point is the Riemann-Siegel formula, which roughly speaking is of the shape where , is an explicit “gamma factor” that decays exponentially in , and is a ratio of gamma functions that is roughly of size . Deforming this by the heat flow gives rise to an approximation ...
Now we'll learn what the alternating se-ries estimation theorem is? A partial sum S,, of any convergent seriescan be used as an approximation to the totalsum. If we want estimate the accuracy of ap-proximation, then the error and remaindershould be considered. The error involved inusing ...
A function f (x) and a value of n are given. Determine a formula for R_n (x) and find a bound for |R_n (x)| on the given interval. This bound for |R_n (x)| is our "guaranteed accuracy" for P_n to appr d. When linear approximation is used to ...
Thread starter okay Start date Dec 9, 2007 Tags Eulers formula Formula In summary, the number e is the limit of the expression (1+\frac{1}{n})^{n} as n grows beyond bound, and it was originally shown to look like that by Euler. Proofs of this are somewhat tricky, but it...
although this is now an antihomomorphism rather than a homomorphism: . One can then split up a quaternion into its real part and imaginary part by the familiar formulae (though we now leave the imaginary part purely imaginary, as opposed to dividing by in the complex case). The inner ...