A Bombieri-Vinogradov theorem for all number fields

M. Ram Murty, Kathleen L. Petersen

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)4987-5032
Number of pages46
JournalTransactions of the American Mathematical Society
Volume365
Issue number9
DOIs
StatePublished - 2013
Externally publishedYes

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