An analogue of Artin's conjecture for Abelian extensions

DOI10.1016/0022-314X(84)90059-3zbMath0531.12010OpenAlexW2032696138WikidataQ123004082 ScholiaQ123004082MaRDI QIDQ788048

M. Ram Murty

Publication date: 1984

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-314x(84)90059-3

zbMATH Keywords

Abelian extensionsGRHArtin conjecture on primitive rootscomplete splitting of primesgeneralized Riemann hypothesis for Dedekind zeta-functions

Mathematics Subject Classification ID

Distribution of integers in special residue classes (11N69) Zeta functions and (L)-functions of number fields (11R42) Density theorems (11R45)

Related Items

Cyclicity of CM elliptic curves modulo 𝑝 ⋮ Explicit Lower bounds for residues at 𝑠=1 of Dedekind zeta functions and relative class numbers of CM-fields ⋮ A finiteness theorem for imaginary abelian number fields ⋮ On the nature of \(e^{\gamma}\) and non-vanishing of derivatives of \(L\)-series at \(s=1/2\) ⋮ Class number problem for imaginary cyclic number fields ⋮ Class numbers of imaginary abelian number fields ⋮ A note on Dedekind zeta values at 1/2 ⋮ On the cyclicity of the group of \({\mathbb F}_p\)-rational points of non-CM elliptic curves

Cites Work

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• Some effective cases of the Brauer-Siegel theorem
• The large sieve
• On Artin's conjecture.
• A Counterexample to an Analogue of Artin's Conjecture

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