A note on the least prime that splits completely in a nonabelian Galois number field
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We prove a nontrivial estimate for the size of the least rational prime that splits completely in the ring of integers of certain families of nonabelian Galois number fields. Our result complements results of Linnik and Vinogradov and of Pollack who studied this problem in the quadratic and abelian number field settings, respectively.
KeywordsPrimes Split completely Number fields Dedekind zeta-function Subconvexity
Mathematics Subject Classification11R42 11R44 11F66 11M20
This project began as a result of an SEC Faculty Travel Grant that allowed the second author to visit the University of Georgia. We thank the Southeastern Conference for its support. We also thank Caroline Turnage-Butterbaugh, Jesse Thorner, and the anonymous referee for a number of useful comments.