Critical zeros of Hecke L-functions

In this dissertation, we established that in average taken over the family of all Hecke L-functions of weight k of size K associated with the full modular group, at least 35% of their zeros lie on the critical line as K → ∞. We used Levinson’s method employing a mollifier of length K^2θ with θ sufficiently close to 1/2. To handle such a long mollifier, it was necessary to develop an Asymptotic Large Sieve that evaluated a bilinear form by taking advantage of sum cancellations resulting from the quasi-orthogonality property of Hecke eigenvalues for a sufficiently large number of weights kPh.D.Includes bibliographical referencesby Jorge Cantill