# Argument Alpha

The Experts below are selected from a list of 6 Experts worldwide ranked by ideXlab platform

### Trevor D. Wooley – 1st expert on this subject based on the ideXlab platform

• ##### Mean value estimates for odd cubic Weyl sums
arXiv: Number Theory, 2014
Co-Authors: Trevor D. Wooley

Abstract:

We establish an essentially optimal estimate for the ninth moment of the exponential sum having Argument $\Alpha x^3+\beta x$. The first substantial advance in this topic for over 60 years, this leads to improvements in Heath-Brown’s variant of Weyl’s inequality, and other applications of Diophantine type.

### William Worden – 2nd expert on this subject based on the ideXlab platform

• ##### Iterations of Quadratic Polynomials over Finite Fields
arXiv: Number Theory, 2012
Co-Authors: William Worden

Abstract:

Given a map f:Z–>Z and an initial Argument Alpha, we can iterate the map to get a finite set of iterates modulo a prime p. In particular, for a quadratic map f(z)=z^2 +c, c constant, work by Pollard suggests that this set should have length on the order of p^(1/2). We give a heuristic Argument that suggests that the statistical properties of this set might be very similar to the Birthday Problem random variable X_n, for an n=p day year, and offer considerable experimental evidence that the limiting distribution of these set lengths, divided by p^(1/2), for p\leq x as x goes to infinity, converges to the limiting distribution of X_n/n^(1/2), as n goes to infinity.