Subconvexity for $GL(3)\times GL(2)$ $L$-functions in $GL(3)$ spectral aspect

Sharma, Prahlad

doi:10.48550/arxiv.2010.10153

Cited by 3 publications

(5 citation statements)

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“…The exponent of saving in the M-aspect was recently improved to 1/32 by Sharma [37]. Following Li's work in [17], there have been recent developments in the subconvexity problem on GL(3) × GL(2) in different aspects, and the reader is referred to [15,16,18,19,31,35,37,38].…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

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

Lin

2021

J. Eur. Math. Soc.

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Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

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

Lin

2021

J. Eur. Math. Soc.

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“…Remark 2.5. The exploitation of invariance in the central direction is reminiscent of the conductor lowering trick applied by Munshi and others to the subconvexity problem on GL 3 (see [Mu1,Mu3,Sh,LMS]). It might be interesting to understand any relation more precisely.…”

Section: Relative Trace Formulamentioning

confidence: 99%

“…Remark 2.10. It would be interesting to understand whether ideas related to the case n = 2 of Theorem 12.3 are implicit in existing proofs of spectral aspect subconvex bounds on GL 3 [BB1,BB2,KMS,Sh].…”

Section: Relative Trace Formulamentioning

confidence: 99%

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Spectral aspect subconvex bounds for ${\rm U}_{n+1} \times {\rm U}_{n}$

Nelson¹

2020

Preprint

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Let (π, σ) traverse a sequence of pairs of cuspidal automorphic representations of an anistropic unitary Gan-Gross-Prasad pair (U n+1 , Un) over a number field. We assume that at some distinguished archimedean place, the pair stays away from the conductor dropping locus, while at every other place, the pair has bounded ramification and satisfies certain local conditions (in particular, temperedness). We prove that the subconvex boundholds for any fixed δ < 1 16n 5 + 56n 4 + 84n 3 + 72n 2 + 28n .Among other ingredients, the proof employs a refinement of the microlocal calculus for Lie group representations developed with A. Venkatesh and an observation of S. Marshall concerning the geometric side of the relative trace formula.

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“…Munshi [27] also established subconvexity for twists L(f × χ,1/2) in the p-aspect, where χ is a primitive Dirichlet character of prime modulus p. Subconvexity in the spectral aspect of f itself is much harder, and even more so when f is self-dual due to a conductor-dropping phenomenon. Blomer and Buttcane [5], Kumar, Mallesham, and Singh [21], and Sharma [30] have established subconvexity for L(1/2,f ) in the spectral aspect of f in many cases, but excluding the self-dual forms.…”

Section: Introduction 1backgroundmentioning

confidence: 99%

MOMENTS AND HYBRID SUBCONVEXITY FOR SYMMETRIC-SQUARE L-FUNCTIONS

Khan

Young²

2021

J. Inst. Math. Jussieu

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We establish sharp bounds for the second moment of symmetric-square L-functions attached to Hecke Maass cusp forms $u_j$ with spectral parameter $t_j$ , where the second moment is a sum over $t_j$ in a short interval. At the central point $s=1/2$ of the L-function, our interval is smaller than previous known results. More specifically, for $\left \lvert t_j\right \rvert $ of size T, our interval is of size $T^{1/5}$ , whereas the previous best was $T^{1/3}$ , from work of Lam. A little higher up on the critical line, our second moment yields a subconvexity bound for the symmetric-square L-function. More specifically, we get subconvexity at $s=1/2+it$ provided $\left \lvert t_j\right \rvert ^{6/7+\delta }\le \lvert t\rvert \le (2-\delta )\left \lvert t_j\right \rvert $ for any fixed $\delta>0$ . Since $\lvert t\rvert $ can be taken significantly smaller than $\left \lvert t_j\right \rvert $ , this may be viewed as an approximation to the notorious subconvexity problem for the symmetric-square L-function in the spectral aspect at $s=1/2$ .

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Subconvexity for $GL(3)\times GL(2)$ $L$-functions in $GL(3)$ spectral aspect

Abstract: Let f be a SL(2, Z) holomorhic Hecke form and π be a SL(3, Z) Maass cusp form with its Langlands parameter µ in generic position i.e. away from Weyl chamber walls and away from self dual forms. We study the second moment j |L(1/2, π j × f )| 2 and deduce the subconvexity bound

Cited by 3 publications

References 15 publications

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

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

Spectral aspect subconvex bounds for ${\rm U}_{n+1} \times {\rm U}_{n}$

MOMENTS AND HYBRID SUBCONVEXITY FOR SYMMETRIC-SQUARE L-FUNCTIONS

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