Number Theory Days in Lille

Session

Analytic-additive number theory

8 juil. 2019, 09:00

Salle de réunion (Université de Lille)

50. A Minkowski-type result for linearly independent subsets of ideal lattices

Gergely Harcos (Alfréd Rényi Institute of Mathematics)

08/07/2019 09:45

We estimate, in a number field, the maximal number of linearly independent elements with prescribed bounds on their valuations. As a by-product, we obtain new bounds for the successive minima of ideal lattices. Our arguments combine group theory, ramification theory, and the geometry of numbers. This is joint work with Mikołaj Frączyk and Péter Maga.

47. On the distribution of the maximum of partial sums of exponential sums

Youness Lamzouri (Université de Lorraine / York University)

08/07/2019 11:00

In analogy with multiplicative character sums, we investigate the distribution of the maximum of partial sums of various families of exponential sums. We obtain precise estimates on the distribution function in a large uniform range, in the case where the Fourier transforms of these exponential sums are real valued, and satisfy some "natural" hypotheses. Important examples include Birch sums...

40. The mean value of cubic L-functions over function fields

Matilde Lalín (Université de Montréal)

08/07/2019 14:00

We present results about the first moment of L-functions associated to cubic characters over ${\mathbb{F}}_q(T)$ when q is congruent to 1 modulo 3. The case of number fields was considered in previous work, but never for the full family of cubic twists over a field containing the third roots of unity. We will explain how to obtain an asymptotic formula with a main term, which relies on using...

51. Bootstrapping partition regularity of linear systems

Tom Sanders (University of Oxford)

08/07/2019 15:30

Suppose that $A$ is a $k\times d$ matrix of integers such that fir any $r$ there is some $N$ such that any $r$-colouring of $\{1,\dots ,N\}$ contains a monochromatic solution to $A$, meaning there is a colour class $C$ and $x\in C^d$ such that $Ax=0$. Not all matrices $A$ have this property (consider, for example, when all the entries of $A$ are positive), but when they do they are called...