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arXiv · 1712.04365

Explicit Burgess-like subconvex bounds for $\mathrm{GL}_2 \times \mathrm{GL}_1$

Wu Han
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Abstract

We make the polynomial dependence on the fixed representation $\pi$ in our previous subconvex bound of $L(1/2,\pi \otimes \chi)$ for $\mathrm{GL}_2 \times \mathrm{GL}_1$ explicit, especially with respect to the usual conductor $\mathbf{C}(\pi_{\mathrm{fin}})$. There is no clue that the original choice, due to Michel & Venkatesh, of the test function at the infinite places should be the optimal one. Hence we also investigate a possible variant of such local choices in some special situations.

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Wu Han. 2017-12-12. Explicit Burgess-like subconvex bounds for $\mathrm{GL}_2 \times \mathrm{GL}_1$. https://doi.org/10.1515/forum-2019-0074

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