Institut Camille Jordan

The research themes of the team can be divided into the following six main directions :

• Automata, words combinatorics, arithmetic of special functions ;
• (Enumerative, algebraic, analytic) combinatorics, special functions and their interactions ;
• Graphs, orders, infinite combinatorics ;
• Additive number theory, additive combinatorics, densities ;
• Algebraic and algorithmic number theory, L functions, ultrametric analysis, Drinfeld modulus ;
• Analytic number theory, zeta functions.

• Multivariate Zeta functions and applications
  Project between CNRS and Japanese Society for Promotion of Science (JSPS). French head of the project : Driss Essouabri. Other ICJ members in the project : Filippo Nuccio, Federico Pellarin, Xavier Roblot

• MZFTTA-Multivariate Zeta functions, Tauberian theorems and Applications
  Scientif cooperation between France and Latin America (MATH-AmSud). International Coordinator, and French head of the project with Brazil : Driss Essouabri.

• B. Adamczewski, J. P. Bell. On vanishing coefficients of algebraic power series over fields of positive characteristic. Invent. Math. 187 (2012), no. 2, 343—393.

• B. Lass. Mehler formulae for matching polynomials of graphs and independence polynomials of clawfree graphs. J. Combin. Theory Ser. B 102 (2012), no. 2, 411—423.

• F. Pellarin. Values of certain L-series in positive characteristic. Ann. of Math. (2)176 (2012), no. 3, 2055—2093.

• M. Barge, L. Q. Zamboni. Central sets and substitutive dynamical systems. Adv. Math. 248 (2013), 308—323.

• C. Delaunay, E. Fricain, E. Mosaki, O. Robert. Zero-free regions for Dirichlet series.Trans. Amer. Math. Soc. 365 (2013), no. 6, 3227—3253.

• D. Essouabri, B. Lichtin. Zeta functions of discrete self-similar sets. Adv. Math. 232 (2013), 142—187.

• M. E. H. Ismail, A. Kasraoui, J. Zeng. Separation of variables and combinatorics of linearization coefficients of orthogonal polynomials. J. Combin. Theory Ser. A 120 (2013), 561—599.

• C. Delaunay, F. Jouhet. pl-torsion points in finite abelian groups and combinatorial identities. Adv. Math. 258 (2014), 13—45.

• F. Pellarin. Estimating the order of vanishing at infinity of Drinfeld quasi-modular forms. J. Reine Angew. Math. 687 (2014), 1—42.

• B. Adamczewski, J. P. Bell. Diagonalization and rationalization of algebraic Laurent series, à paraître aux Ann. Sci. Éc. Norm. Supér., 49 pp.