The Burgess bound via a trivial delta method

Aggarwal, Keshav; Holowinsky, Roman; Lin, Yongxiao; Sun, Qingfeng

doi:10.1007/s11139-020-00258-x

Cited by 15 publications

(17 citation statements)

References 12 publications

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“…Plugging the leading term of the above Lemma 5.2 in Lemma 5.1 and using the resulting expression in (4) we see that the sum over n transform into…”

Section: Gl(3) Voronoimentioning

confidence: 99%

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Sub-convexity bound for $GL(3) \times GL(2)$ $L$-functions: Hybrid level aspect

Kumar¹,

Munshi²,

Singh³

2021

Preprint

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“…Plugging the leading term of the above Lemma 5.2 in Lemma 5.1 and using the resulting expression in (4) we see that the sum over n transform into…”

Section: Gl(3) Voronoimentioning

confidence: 99%

“…After initial success of the second author [27], the method has been extended, simplified and generalised by several researchers, e.g. see [14], [2], [3], [4], [18], [19], [29], [30] and [23].…”

Section: Introductionmentioning

confidence: 99%

Sub-convexity bound for $GL(3) \times GL(2)$ $L$-functions: Hybrid level aspect

Kumar¹,

Munshi²,

Singh³

2021

Preprint

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“…Less standardly, we write A ≺ B or B ≻ A as shorthand for A ≪ q o(1) B, or equivalently, |A| q o(1) |B|. Our goal is then to show that L(π ⊗ χ, 1 2 ) ≺ q 3/4−δ0 .…”

Section: Preliminariesmentioning

confidence: 99%

“…where G ± is meromorphic on C and holomorphic in the domain Re(s) > 5/14, where it satisfies G ± (s) ≪ (1 + |s|) O (1) for fixed Re(s). (The indices n and d in (2.2) are implicitly restricted to be positive integers.)…”

Section: General Notationmentioning

confidence: 99%

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Subconvex bounds on GL(3) via degeneration to frequency zero

Holowinsky¹,

Nelson²

2018

Preprint

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For a fixed cusp form π on GL 3 (Z) and a varying Dirichlet character χ of prime conductor q, we prove that the subconvex bound2 ) ≪ q 3/4−δ holds for any δ < 1/36. This improves upon the earlier bounds δ < 1/1612 and δ < 1/308 obtained by Munshi using his GL 2 variant of the δ-method. The method developed here is more direct. We first express χ as the degenerate zero-frequency contribution of a carefully chosen summation formula à la Poisson. After an elementary "amplification" step exploiting the multiplicativity of χ, we then apply a sequence of standard manipulations (reciprocity, Voronoi, Cauchy-Schwarz and the Weil bound) to bound the contributions of the nonzero frequencies and of the dual side of that formula. Contents 1. Introduction 2. Preliminaries 3. Division of the proof 4. Estimates for F 5. Estimates for O Appendix A. Correlations of Kloosterman sums Appendix B. Comparison with Munshi's approach References

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Subconvex bounds on $${{\mathrm{GL}}}_3$$ GL 3 via degeneration to frequency zero

Holowinsky

Nelson

2018

Math. Ann.

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For a fixed cusp form π on GL 3 (Z) and a varying Dirichlet character χ of prime conductor q, we prove that the subconvex bound L π ⊗ χ, 1 2 q 3/4−δ holds for any δ < 1/36. This improves upon the earlier bounds δ < 1/1612 and δ < 1/308 obtained by Munshi using his GL 2 variant of the δ-method. The method developed here is more direct. We first express χ as the degenerate zero-frequency contribution of a carefully chosen summation formula à la Poisson. After an elementary "amplification" step exploiting the multiplicativity of χ , we then apply a sequence of standard manipulations (reciprocity, Voronoi, Cauchy-Schwarz and the Weil bound) to bound the contributions of the nonzero frequencies and of the dual side of that formula.

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The Burgess bound via a trivial delta method

Cited by 15 publications

References 12 publications

Sub-convexity bound for $GL(3) \times GL(2)$ $L$-functions: Hybrid level aspect

Sub-convexity bound for $GL(3) \times GL(2)$ $L$-functions: Hybrid level aspect

Subconvex bounds on GL(3) via degeneration to frequency zero

Subconvex bounds on $${{\mathrm{GL}}}_3$$ GL 3 via degeneration to frequency zero

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