On the Chebotarev–Sato–Tate phenomenon

We study the Chebotarev–Sato–Tate phenomenon that concerns the distribution of Artin symbols and Frobenius angles. From the recent work of Barnet-Lamb et al., we derive some unconditional results in the case of Hilbert modular forms. Furthermore, under the Langlands functoriality conjecture and the...

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Bibliographic Details
Published in:Journal of number theory 2019-03, Vol.196, p.272-290
Main Author: Wong, Peng-Jie
Format: Article
Language:English
Subjects:
Automorphic L-functions
Chebotarev–Sato–Tate distribution
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Summary:We study the Chebotarev–Sato–Tate phenomenon that concerns the distribution of Artin symbols and Frobenius angles. From the recent work of Barnet-Lamb et al., we derive some unconditional results in the case of Hilbert modular forms. Furthermore, under the Langlands functoriality conjecture and the generalised Riemann hypothesis, we give two effective versions of such distributions, which present a modular variant of the results of Bucur, Kedlaya, and V.K. Murty.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2018.09.010