1 results
Burgess-like subconvexity for
$\text{GL}_{1}$
- Part of
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- Journal:
- Compositio Mathematica / Volume 155 / Issue 8 / August 2019
- Published online by Cambridge University Press:
- 04 July 2019, pp. 1457-1499
- Print publication:
- August 2019
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- Article
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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.
