Central L-values of Maass wave forms

Speaker: 刘慎徽(University of Toronto)

Venue: B1044

Time: 2017年12月15日   14:00-15:00

Title: Central L-values of Maass wave forms

Abstract: In this talk, I will focus on central L-values of Maass wave forms and present a positive-proportional nonvanishing result of such values in the aspect of large spectral parameter in short intervals, which is qualitatively optimal in view of Weyl’s law. The result is obtained by studying mollified moments with the Kuznetsov trace formula (for the first moment) and a formula of Motohashi (for the second moment). As an application of this result and a formula of Katok–Sarnak, I will give a nonvanishing result of the first Fourier coefficients of Maass forms of weight 1/2 and level 4 in the Kohnen plus space.