Short second moment bound and subconvexity for $\mathrm{GL}(3)$ $L$-functions

Keshav Aggarwal; Wing Hong Leung; Ritabrata Munshi

doi:10.4171/jems/1667

JournalsjemsVol. 28, No. 11pp. 4797–4871

Short second moment bound and subconvexity for $GL (3)$ $L$ -functions

Keshav Aggarwal
Indian Institute of Technology Bombay, Mumbai, India
- MR
Wing Hong Leung
Rutgers University, Piscataway, USA
- MR
- ORCID
Ritabrata Munshi
Indian Statistical Institute, Kolkata, India
- MR

$Short second moment bound and subconvexity for $\mathrm{GL}(3)$ $L$-functions cover$

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Abstract

Let $π$ be a Hecke cusp form for $SL (3, Z)$ . We bound the second moment average of $L (s, π)$ over a short interval to obtain the subconvexity estimate

L (1/2 + i t, π) ≪_{π, ε} (1 + ∣ t ∣)^{3/4 - 1/8 + ε} .

This is the first time a short second moment has been used to obtain a subconvexity bound in a higher rank group.

Cite this article

Keshav Aggarwal, Wing Hong Leung, Ritabrata Munshi, Short second moment bound and subconvexity for $GL (3)$ $L$ -functions. J. Eur. Math. Soc. 28 (2026), no. 11, pp. 4797–4871

DOI 10.4171/JEMS/1667