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A vertical Sato-Tate law for GL(4)

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Abstract

We establish a doubly-weighted vertical Sato-Tate law for GL(4) with explicit error terms. The main ingredient is an extension of the orthogonality relation for Maass cusp forms on GL(4) of Goldfeld, Stade, and Woodbury from spherical to general forms, and without their assumption of the Ramanujan conjecture for the error term.

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Acknowledgements

The author thanks Jack Buttcane and Keshav Aggarwal for helpful conversations related to this work. The author was partially supported by NSF grant DMS-2212924.

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  1. University of Michigan-Dearborn, Dearborn, MI, 48128, USA

    Tian An Wong

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  1. Tian An Wong
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Correspondence to Tian An Wong.

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Wong, T.A. A vertical Sato-Tate law for GL(4). Arch. Math. (2024). https://doi.org/10.1007/s00013-024-01996-w

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  • DOI: https://doi.org/10.1007/s00013-024-01996-w

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