Hybrid bounds for twisted L-functions

By V. Blomer, Gergely Harcos. 2008

119 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Artificial Intelligence, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4cd46eced826be2887e02599fa0bff4300f7bb2f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. M. Young
2. R. Munshi
3. V. Blomer
4. Ian Petrow
5. Djordje Milićević
6. Gergely Harcos
7. P. Michel
8. Peter Sarnak

In Artificial Intelligence

1. R. Munshi
2. M. Young
3. V. Blomer
4. Ian Petrow
5. Gergely Harcos
6. Djordje Milićević
7. P. Michel
8. Emmanuel Kowalski

In Mathematical Physics

1. M. Young
2. R. Munshi
3. V. Blomer
4. Ian Petrow
5. Djordje Milićević
6. Gergely Harcos
7. P. Michel
8. Akshay Venkatesh

Citations in the corpus

• Weyl-type hybrid subconvexity bounds for twisted $L$-functions and Heegner points on shrinking sets (2014, background): “lytic conductor of L(uj × χq,1/2) is q2(1 + T2). The previously best-known subconvexity bound for these twisted L-functions with uniformity in both qand T(or k) is apparently due to Blomer and Harcos [BH]. Their bound is of Burgess quality, meaning that in the q-aspect the exponent is 3/8+ε instead ”
• Twisted L-Functions Over Number Fields and Hilbert’s Eleventh Problem (2009, methodology): “rder to bound the Fourier coefficients of half-integral weight Hilbert modular forms. For K = Q, the original breakthrough was achieved by Iwaniec [Iw1], and the currently strongest bounds are given in [BH1]. For a totally real number field Kother than Q, there does not seem to be an explicit reference”
• The Second Moment of Twisted Modular L-Functions (2014, background): “e first instance of any simultaneous non-vanishing result for general twists of automorphic L-functions. The quantitative version comes from the best-known subconvexity results for twisted L-functions [BH2]. As another application of the asymptotic formula in Theorem 1 — and here the power saving is ”
• The Weyl bound for Dirichlet L-functions of cube-free conductor (2018, background): “finite 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”
• A generalized cubic moment and the Petersson formula for newforms (2016, background): “ cU(n) = 0. If nis locally represented everywhere by Q, then cE(n) ≫Qn1/2−ε. Theorem 1.3 implies cS(n) ≪Qn5/12+ε, which is an improvement over that derived from the Burgess-quality subconvex bound of [BH] . For some more advanced questions, one may desire to explicate the dependence on gin Theorem 1”
• The circle method and bounds for L-functions---II: Subconvexity for twists of GL(3) L-functions (2012, methodology): “The first hybrid subconvex bound was given by Blomer and Harcos [1].”