We bound a short second moment average of `$\mathrm{GL}(3)$`

and `$\mathrm{GL}(3) \times \mathrm{GL}(1)$`

`$L$`

-functions. These yield `$t$`

-aspect and depth aspect subconvexity bounds respectively, and improve upon the earlier subconvexity exponents. This moment estimate provides an analogue for cusp forms of Ivicâ€™s bound for the sixth moment of the zeta function, and is the first time a short second moment has been used to obtain a subconvex bound in higher rank. This is a joint work with Ritabrata Munshi and Wing Hong Leung.

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Last updated: 23 Feb 2024