Abstract
Abstract We make the polynomial dependence on the fixed representation π in our previous subconvex bound of L ( 1 2 , π ⊗ χ ) {L(\frac{1}{2},\pi\otimes\chi)} for GL 2 × GL 1 {\mathrm{GL}_{2}\times\mathrm{GL}_{1}} explicit, especially in terms of the usual conductor 𝐂 ( π fin ) {\mathbf{C}(\pi_{\mathrm{fin}})} . There is no clue that the original choice, due to Michel and 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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