Explicit Burgess-like subconvex bounds for GL2 × GL1

  • 1 School of Mathematical Sciences, Queen Mary University of London, Mile End Road, Stepney, London, United Kingdom
Han WuORCID iD: https://orcid.org/0000-0001-5140-3174

Abstract

We make the polynomial dependence on the fixed representation π in our previous subconvex bound of L(12,πχ) for GL2×GL1 explicit, especially in terms of the usual conductor 𝐂(πfin). 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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