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Johannes Linn

Publications and source records attributed to Johannes Linn.

2 recordsLinked to original sources
arXiv2026

Symmetric square $L$-functions on $\mathrm{GL}_3$

We give an asymptotic formula with a power-saving error term for the twisted first moment of symmetric square $L$-functions on $\mathrm{GL}_3$ in the spectral aspect. We apply this to obtain non-vanishing results and lower bounds of the expected order of magnitude for even moments, supporting the random matrix model for a unitary ensemble of $L$-functions. The main ingredients are the $\mathrm{GL}_3$ Kuznetsov formula, an asymmetric approximate functional equation, and strong bounds for the integral transforms appearing in the Kuznetsov formula.

math.NT↗
arXiv2025

Bounds for Kloosterman Sums for $\mathrm{GL}_n$

In this paper power saving bounds for general Kloosterman sums for all Weyl elements for $\mathrm{GL}_n$ for $n>2$ are proven, improving the trivial bound by Dąbrowski and Reeder. This is achieved by representing the sums in an explicit way as exponential sums and bounding these through applications of the Weil bound.

math.NT↗