A Bombieri-Vinogradov theorem for all number fields

Murty, M.; Petersen, Kathleen

doi:10.1090/S0002-9947-2012-05805-3

A Bombieri-Vinogradov theorem for all number fields
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by M. Ram Murty and Kathleen L. Petersen PDF

Trans. Amer. Math. Soc. 365 (2013), 4987-5032 Request permission

Abstract:

The classical theorem of Bombieri and Vinogradov is generalized to a non-abelian, non-Galois setting. This leads to a prime number theorem of “mixed-type” for arithmetic progressions “twisted” by splitting conditions in number fields. One can view this as an extension of earlier work of M. R. Murty and V. K. Murty on a variant of the Bombieri-Vinogradov theorem. We develop this theory with a view to applications in the study of the Euclidean algorithm in number fields and arithmetic orbifolds.

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