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A note on Maass forms of icosahedral type

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Original languageEnglish
Pages (from-to)1315-1324
Number of pages10
JournalMathematische Zeitschrift
Volume292
Issue number3-4
Early online date24 Oct 2018
DOIs
DateAccepted/In press - 13 Aug 2018
DateE-pub ahead of print - 24 Oct 2018
DatePublished (current) - 1 Aug 2019

Abstract

Using ideas of Ramakrishnan, we consider the icosahedral analogue of the theorems of Sarnak and Brumley on Hecke–Maass newforms with Fourier coefficients in a quadratic order. Although we are unable to conclude the existence of an associated Galois representation in this case, we show that one can deduce some implications of such an association, including weak automorphy of all symmetric powers and the value distribution of Fourier coefficients predicted by the Chebotarev density theorem.

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    Rights statement: This is the final published version of the article (version of record). It first appeared online via Springer at https://doi.org/10.1007/s00209-018-2157-3 . Please refer to any applicable terms of use of the publisher.

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