Number theory days

Session

Analytic-Additive Number Theory

23 juin 2014, 10:00

Salle de réunions (Université Lille 1)

Présidents de session

Analytic-Additive Number Theory

• Gautami Bhowmik (Université Lille 1)

21. Sign changes of Fourier coefficients of cusp forms

Winfried Kohnen (Universität Heidelberg)

23/06/2014 10:00

Analytic-Additive Number Theory

We will give a survey on recent results about sign changes of Fourier coefficients of cusp forms in one and several variables.

13. Generalised Fourier coefficients of multiplicative functions

Lilian Matthiesen (Institut de Mathématiques de Jussieu)

23/06/2014 11:30

Analytic-Additive Number Theory

The aim of this talk is to explain a strategy that allows us to bound the Fourier coefficients of a large class of not necessarily bounded multiplicative functions. The interest in this result lies in the fact that the strategy can be adapted to show that these multiplicative functions give rise to functions that are orthogonal to linear nilsequences when applying a `W-trick'. This, in turn,...

16. On the history of analytic number theory

Catherine Goldstein (Institut de mathématiques de Jussieu)

23/06/2014 14:30

Analytic-Additive Number Theory

Contrarily to other parts of number theory, the history of analytic number theory often appears as a collection of particular, even isolated, episodes, focussing on Euler or Riemann or Hadamard and de La Vallée-Poussin. The talk will discuss some of these gems, as well as less well-known ones, and comment on the discontinuous character of their history.

15. Some Problems in Analytic Number Theory for Polynomials over Finite Fields

Julio Andrade (IHES)

23/06/2014 15:45

Analytic-Additive Number Theory

In this talk I will explore some traditional problems of analytic number theory in the context of function fields over a finite field. Several such problems which are currently viewed as intractable can, in the function field scenario, be attacked with vastly different tools than those of traditional analytic number theory. The resulting theorems in the function field setting can be used to...

11. Phénomènes de seuil pour les suites de pseudo puissances

Alain Plagne (École polytechnique)

23/06/2014 17:15

Analytic-Additive Number Theory

Nous étudions des phénomènes de seuil en théorie additive des nombres. L'objet central est les pseudo puissances s-ièmes introduites par Erdos et Renyi en 1960. In 1975, Goguel a montré que, presque surement, une telle suite n'était pas une base asymptotique d'ordre s. On verra qu'elle est presque surement base d'ordre s+\epsilon. On étudie aussi la taille du plus petit complément additif de...