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تسجيل مستخدم جديدHybrid subconvexity for class group $L$-functions and uniform sup norm bounds of Eisenstein series
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In this paper we prove a hybrid subconvexity bound for class group $L$-functions associated to a quadratic extension $K/mathbb{Q}$ (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 following uniform sup norm bound for Eisenstein series $E(z,1/2+it)ll_varepsilon y^{1/2} (|t|+1)^{1/3+varepsilon}, ygg 1$, extending work of Blomer and Titchmarsh. Finally, we propose a uniform version of the sup norm conjecture for Eisenstein series.
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