Extreme values for divisor functions

On the Distribution of Values of Certain Divisor Functions

Let {Ed} be a sequence of nonnegative numbers and f(n) = E Ed , the suns being over divisors d of n. We say that f has the distribution function F if for all c > 0, the number of integers n c x for which f (n) > c is asymptotic to xF(c), and we investigate when F exists and when it is continuous. Let {E d } be a sequence of nonnegative numbers and Is it true that for all c > 0, f (n) _ y Ed. di...

Smooth functions and local extreme values

Given a sample of n observations y1, . . . , yn at time points t1, . . . , tn we consider the problem of specifying a function f̃ such that f̃ • is smooth, • fits the data in the sense that the residuals yi − f̃(ti) satisfy the multiresolution criterion

Extreme Values of Zeta and L-functions

Extreme values of Artin L-functions and class numbers

Assuming the GRH and Artin conjecture for Artin L-functions, we prove that there exists a totally real number field of any fixed degree (> 1) with an arbitrarily large discriminant whose normal closure has the full symmetric group as Galois group and whose class number is essentially as large as possible. One ingredient is an unconditional construction of totally real fields with small regulato...

Free Extreme Values

Free probability analogues of the basics of extreme value theory are obtained, based on Ando’s spectral order. This includes classification of freely max-stable laws and their domains of attraction, using “free extremal convolutions” on the distributions. These laws coincide with the limit laws in the classical peaks-over-threshold approach. A free extremal projection-valued process over a meas...