Bounds for twists of $\rm GL(3)$ $L$-functions

Lin, Yongxiao

doi:10.48550/arxiv.1802.05111

Cited by 7 publications

(13 citation statements)

References 23 publications

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“…On the other hand, our result in t-aspect doesn't need a 'conductor lowering' trick. Other works that deal with the subconvex bound problem for degree three L-functions include [2,5,9,[12][13][14][15][16]19].We start with applying the approximate functional equation (Lemma 3.1)…”

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confidence: 99%

A new subconvex bound for $\rm GL(3)$ $L$-functions in the $t$-aspect

Aggarwal

2019

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We revisit Munshi's proof of the t-aspect subconvex bound for GLp3q L-functions, and we are able to remove the 'conductor lowering' trick. This simplification along with a more careful stationary phase analysis allows us to improve Munshi's bound to,By choosing q to be of size approximately t 1{3 , one can get the Weyl bound for GLp2q L-functions in t-aspect. This circle method seems insufficient to obtain a GLp3q t-aspect subconvex bound, so we use Kloosterman's version of the circle method (Lemma 1.2).A t-aspect bound for self-dual GLp3q L-functions was first established by Li [8], and improved upon by McKee, Sun and Ye [10], Sun and Ye [19] and Nunes [17]. A t-aspect bound for a general SLp3, Zq L-function was proved by Munshi by a completely different approach. We revisit Munshi's proof and improve upon his result. Although the bound obtained here is weaker than that in [10,17,19], it holds for any Hecke-Maass cusp form for SLp3, Zq, and not just the self-dual forms. We note that we get the same exponent as Sun and Zhao [20], whose work is on bounding twists of GLp3q L-functions in depth aspect. They use Kloosterman's version of circle method, along with a 'conductor lowering' trick appropriate for the depth aspect. On the other hand, our result in t-aspect doesn't need a 'conductor lowering' trick. Other works that deal with the subconvex bound problem for degree three L-functions include [2,5,9,[12][13][14][15][16]19].We start with applying the approximate functional equation (Lemma 3.1)

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confidence: 99%

A new subconvex bound for $\rm GL(3)$ $L$-functions in the $t$-aspect

Aggarwal

2019

Preprint

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“…Due to the introduction of new methods in recent years, the problem has attracted considerable attention, see e.g. [1,3,13,15,16]. All these methods proved results for cusp forms of full level, and some could be adopted to prove a t-aspect bound for square-free level.…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

“…He would further like to thank Prof. Holowinsky for his support and encouragement. This paper branched out while working with Lin and Holowinsky to apply the method of degeneration to frequency zero to SLp2, Zq L-functions as done in [7,13].…”

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Weyl bound for $\rm GL(2)$ in $t$-aspect via a trivial delta method

Aggarwal¹

2018

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We use a 'trivial' delta method to prove the Weyl bound in t-aspect for the L-function of a holomorphic or a Hecke-Maass cusp form of arbitrary level and nebentypus. In particular, this extends the results of Meurman and Jutila for the t-aspect Weyl bound, and the recent result of Booker, Milinovich and Ng to Hecke cusp forms of arbitrary level and nebentypus.2010 Mathematics Subject Classification. 11F66.

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“…For subconvexity results for GL 3 over Q without the self-dual assumption, we refer the reader to the papers of Munshi,Holowinsky,Nelson,Yongxiao Lin,et. al.,[Mun1,Mun2,Mun3,Mun4,HN,Lin,SZ,Agg,Sha,LS,Sch].…”

Section: Introductionmentioning

confidence: 99%