Joint extreme values of L-functions

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...

EXTREME VALUES OF arg L ( 1 , χ )

Values of Dirichlet L-functions at s = 1 have always attracted great attention due to their central role in number theory. In particular the prime number theorem for arithmetic progressions relies on the non-vanishing of L(1, χ) for any non-principal character χ (mod q). Moreover improving the existing lower bounds for |L(1, χ)| (the famous Siegel’s bound |L(1, χ)| ≫ǫ q) would imply many import...

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

On the Distribution of Extreme Values of Zeta and L-functions in the Strip

Abstract. We study the distribution of large (and small) values of several families of L-functions on a line Re(s) = σ where 1/2 < σ < 1. We consider the Riemann zeta function ζ(s) in the t-aspect, Dirichlet L-functions in the q-aspect, and L-functions attached to primitive holomorphic cusp forms of weight 2 in the level aspect. For each family we show that the L-values can be very well modeled...