Burgess-like Subconvex Bounds for GL2 × GL1

By Han Wu. 2012

46 citations recorded by the source corpus.

Let F be a number field, π an irreducible cuspidal representation of $${{\rm GL}_2(\mathbb{A}_F)}$$GL2(AF) with unitary central character, and χ a Hecke character of analytic conductor Q. Then $${L(1/2, \pi \otimes \chi) \ll Q^{\frac{1}{2} - \frac{1}{8}(1-2\theta)+\epsilon}}$$L(1/2,π⊗χ)≪Q12-18(1-2θ)+ϵ, where $${0 \leq \theta \leq 1/2}$$0≤θ≤1/2 is any exponent towards the Ramanujan–Petersson conjecture. The proof is based on an idea of unipotent translation originated from P. Sarnak then developed by Ph. Michel and A. Venkatesh, combined with a method of amplification.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/207c763c11af6163b8299a7fddf8c2d359f29469

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In Algebra and Number Theory

1. Ian Petrow
2. M. Young
3. Siegfred Baluyot
4. Stephan Baier
5. Manjul Bhargava
6. A. Shankar
7. Alexandra Florea

In Discrete Mathematics and Combinatorics

1. Ian Petrow
2. M. Young
3. Stephan Baier

In Mathematical Physics

1. Ian Petrow
2. M. Young
3. Alexandra Florea

Citations in the corpus

• The Weyl bound for Dirichlet L-functions of cube-free conductor (2018, background): “ fields. Note that the Burgess exponent of 3/16 falls short of the exponent 1/6 found by Weyl. Curiously, the exponent 3/16 often re-occurs in the modern incarnations of these problems, see [BHM] [BH] [Wu1] [Wu2] for example. Even for the case of Dirichlet L-functions, the Burgess bound has only been”