Statistics for low-lying zeros of Hecke L -functions in the level aspect

Guillaume Ricotta (1)

1 IMB - Institut de Mathématiques de Bordeaux

In this paper, we remind you of Iwaniec-Luo-Sarnak's results on one-level densities for low-lying zeros of Hecke L-functions and Katz-Sarnak's results on one-level densities for eigenvalues of orthogonal random matrices. Then, we introduce you to a very strange phenomenom discovered by Hughes and Miler: Mock-Gaussian behaviour.

Domaines: Théorie des nombres [math.NT]

Guillaume Ricotta. Statistics for low-lying zeros of Hecke L -functions in the level aspect. Mathematisches Forschungsinstitut Oberwolfach, 2007, Report (n° 34/2007), pp.19--24. ⟨hal-00354958⟩