Forum Mathematicum ( IF 0.733 ) Pub Date : 2020-11-04 , DOI: 10.1515/forum-2019-0173
Asbjørn Christian Nordentoft

In this paper, we study hybrid subconvexity bounds for class group 𝐿-functions associated to quadratic extensions $K/Q$ (real or imaginary). Our proof relies on relating the class group 𝐿-functions to Eisenstein series evaluated at Heegner points using formulas due to Hecke. The main technical contribution is the uniform sup norm bound for Eisenstein series $E⁢(z,1/2+i⁢t)≪εy1/2⁢(|t|+1)1/3+ε$, $y≫1$, extending work of Blomer and Titchmarsh. Finally, we propose a uniform version of the sup norm conjecture for Eisenstein series.

down
wechat
bug