Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH
Copyright policy )Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH
We have proved recently several explicit versions of the prime ideal theorem under GRH. Here we prove a version with optimal asymptotic behaviour.
Followed referee's advice including changing title
- University of Milan Italy
- University of Bergamo Italy
11R42: Zeta functions and $L$-functions of number fields; 11Y40: Algebraic number theory computations, discriminant, Dedekind zeta functions, Mathematics - Number Theory, explicit bounds, Chebyshev function, Algebraic number theory computations, Dedekind functions, GRH, 11R42 (Primary), 11Y70 (Secondary), 11Y70, prime ideal theorem, sharper bounds, prime ideal theorem; Dedekind functions; explicit bounds; GRH, FOS: Mathematics, Zeta functions and \(L\)-functions of number fields, Number Theory (math.NT), 11R42
11R42: Zeta functions and $L$-functions of number fields; 11Y40: Algebraic number theory computations, discriminant, Dedekind zeta functions, Mathematics - Number Theory, explicit bounds, Chebyshev function, Algebraic number theory computations, Dedekind functions, GRH, 11R42 (Primary), 11Y70 (Secondary), 11Y70, prime ideal theorem, sharper bounds, prime ideal theorem; Dedekind functions; explicit bounds; GRH, FOS: Mathematics, Zeta functions and \(L\)-functions of number fields, Number Theory (math.NT), 11R42
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