ED Mathématiques et Informatique
Big prime factors of linear recurrent sequences
by Haojie HONG (IMB - Institut de Mathématiques de Bordeaux)
The defense will take place at 15h00 - Institut de Mathématiques de Bordeaux TBA Université de Bordeaux 351, cours de la Libération 33 405 TALENCE
in front of the jury composed of
- Yuri BILU - Professeur des universités - Université de Bordeaux - Directeur de these
- Sara CHECCOLI - Maîtresse de conférences - Université Grenoble Alpes - Rapporteur
- Aurélien GALATEAU - Maître de conférences - CY Cergy Paris Université - Rapporteur
- Jean GILLIBERT - Professeur - Université Toulouse Jean Jaurès - Examinateur
- Florent JOUVE - Professeur des universités - Université de Bordeaux - Examinateur
This thesis is about lower bounds for the biggest prime divisors of linear recurrent sequences. First, we obtain a uniform and explicit version of Stewart's seminal result about prime divisors of Lucas sequences. We show that constants in Stewart's theorem depend only on the quadratic field corresponding to a Lucas sequence but not on any other parameters. Then we study the prime divisors of orders of elliptic curves over finite fields. Fixing an elliptic curve over a finite field $F_q$ with $q$ power of a prime number, the sequence $# E(F_{q^n})$ happens to be a linear recurrent sequence of order $4$. A lower bound of $P(# E(F_{q^n}))$ is given by using Stewart's argument and some more delicate discussions. Next, motivated by our previous two projects, we can show that when $ gamma $ is an algebraic number of degree 2 and not a root of unity, there exists a prime ideal $ gerp $ of $ Q(gamma) $ satisfying $ u_gerp(gamma^n-1)$, such that the rational prime $p$ underlying $gerp$ grows quickerthan $n$. Finally, we consider a numerical application of Stewart's method to Fibonacci numbers $ F_n $. Relatively sharp bounds for $ P(F_n)$ are obtained. All of the above work relies heavily on Yu's estimate for $p$-adic logarithmic forms.
The Littlewood problem and non-harmonic Fourier series
by Chadi SABA (IMB - Institut de Mathématiques de Bordeaux)
The defense will take place at 14h00 - Salle de conférence Institut de mathématiques de Bordeaux
in front of the jury composed of
- KARIM KELLAY - Professeur des universités - Université de Bordeaux - Directeur de these
- Philippe JAMING - Professeur des universités - Université de Bordeaux - CoDirecteur de these
- Alexander BORICHEV - Professeur des universités - Aix Marseille université - Examinateur
- Pascal LEFEVRE - Professeur des universités - Université d'Artois - Rapporteur
- Jasmin RAISSY - Professeur des universités - Université de Bordeaux - Examinateur
- Jasson VINDAS - Professeur des universités - Ghent University - Rapporteur
- Anne DE ROTON - Maîtresse de conférences - Université de Lorraine - Examinateur
We give some inequalities about $L^1$-norms of non-harmonic trigonometric polynomials. The first one is a quantitative version of a result by Nazarov which also covers the solution of Littlewood conjecture by McGehee, Pigno and Smith. We obtained similar inequalities for quadratic frequencies, lacunary sums and frequencies having multidimensional structure. Furthermore, we give $L^1$-analogue of Kahane's result on the $L^2$-norm of sparse trigonometric polynomials, which we also apply on the Schrödinger equation.
ED Entreprise Economie Société
Digitalization of bank and finance in Africa.
by Safilidin KERE (BSE - Bordeaux sciences économiques)
The defense will take place at 14h00 - Salle des Thèses 16 Avenue Léon Duguit 33600 Pessac
in front of the jury composed of
- Jean-Marc FIGUET - Professeur des universités - Université de Bordeaux - Directeur de these
- François Seck FALL - Professeur des universités - Université de Toulouse Jean Jaurès - Rapporteur
- Jean François BRUN - Maître de conférences - Université Clermont Auvergne - Rapporteur
- Didier ZOUNGRANA - Professeur des universités - Université Thomas Sankara - Examinateur
- Eric ROUGIER - Professeur des universités - Université de Bordeaux - Examinateur
- François COMBARNOUS - Professeur des universités - Université de Bordeaux - Examinateur
This doctoral thesis examines the effects of digitalization on economic development in Africa. It contributes to the empirical analysis of the effects of digital technologies adoption on financial inclusion and economic development. In Chapter 2, we investigate the impacts of the digitalization of financial services on financial inclusion in Africa. The results indicate that mobile money and digital payments have a positive and significant impact on banking rates, access to credit, and savings mobilization. Chapter 3 is an extension of the first chapter on financial inclusion. We empirically analyze the effects of ICT usage on business credit access in Sub-Saharan Africa (SSA). On one hand, the results show that mobile phone subscription, fixed broadband subscription, and individual internet usage have positive effects on credit granted to the private sector. On the other hand, the results also reveal that mobile phone subscription, internet access, and internet usage are associated with the increase in bank loans in Africa. Chapter 4 explores the empirical impact of ICT adoption on trade between SSA countries from 2000 to 2018. The results suggest that ICT usage, especially Internet usage, has positive and significant effects on exports and negative effects on imports of primary products and the total of goods. Within the framework of the free trade agreement adopted by the African Union, this chapter demonstrates the role of digital tools in the success of this important instrument. Finally, in Chapter 5, we assess the impact of mobile money adoption on inflation and economic growth in Africa through a Difference-in-Differences (DiD) model. The results show that mobile money facilitates money circulation, thereby stimulating economic activity without causing an uncontrolled increase in inflation. They also reveal that the adoption of mobile money contributes to the economic growth of countries that have adopted it.