This is a short survey of the known results on classifying finite subsets of an (abelian) additive group or a (not necessarily abelian) multiplicative group that have small doubling in the sense that the sum set or product set is small. Such sets behave approximately like finite subgroups of...
With elementary numerics, we check that the slope of a best fit line through |ζ(it)|2on a log-log plot is indeed 1, to the fourth decimal. We also note that truncating the Riemann zeta function sum at a finite integerNcauses the would-be-eternal ramp to end on a plateau.Suman ...
So it is natural to impose the requirement that be surjective, giving the following commutative diagram to complete: If no further requirements are placed on the lift , then the axiom of choice is precisely the assertion that the lifting problem is always solvable (once we require to be ...
What is the trapezium rule?What are trapeziums?Trapeziums are a form of quadrilateral sharing the same properties as the others in terms or number of sides (4), and sum of the measure of its angles (360{eq}^{\circ} {/eq}). In calculus, trapeziums are very useful as they are the...
Lastly, how does the Riemann Zeta function at “-1”, being the sum of natural numbers, and equaling -1/12 (instead of ‘infinity’?), fit into all this? Thanks, John. Frank Wetzels says: February 2, 2016 at 7:19 pm @ John: Let’s define two s...
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What is upstream vertical integration? What is the fundamental period of the function e^{\cos x + \sin x} ?. How can we find the area of a function f(x)=x^2+x from a to b by Riemann Sums method and relate it to the integral method?
It is assumed that the holographic complexities such as the complexity-action (CA) and the complexity-volume (CV) conjecture are dual to complexity in fiel
"dx" here is still an infinitesimal change in x. To see why it's there, we should think of the integral as a signed area and as the limit of Riemann sums. We recall that to compute a left Riemann sum of f(x) from x=a to x=b with n intervals, we let the following be true...
Numbers in the complex plane can also be inputs to the Riemann Zeta function – for each point in this 2D plane you can evaluate what the function would be equal to for that input. The thing analysts are often interested in when studying a function is where it’s equal to zero – thes...