Abstract
We generalize our previous method on the subconvexity problem for
$\text{GL}_{2}\times \text{GL}_{1}$
with cuspidal representations to Eisenstein series, and deduce a Burgess-like subconvex bound for Hecke characters, that is, the bound
$|L(1/2,\unicode[STIX]{x1D712})|\ll _{\mathbf{F},\unicode[STIX]{x1D716}}\mathbf{C}(\unicode[STIX]{x1D712})^{1/4-(1-2\unicode[STIX]{x1D703})/16+\unicode[STIX]{x1D716}}$
for varying Hecke characters
$\unicode[STIX]{x1D712}$
over a number field
$\mathbf{F}$
with analytic conductor
$\mathbf{C}(\unicode[STIX]{x1D712})$
. As a main tool, we apply the extended theory of regularized integrals due to Zagier developed in a previous paper to obtain the relevant triple product formulas of Eisenstein series.
Subject
Algebra and Number Theory
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