A mean value theorem for cubic fields

Research output: Contribution to journalArticle

Abstract

Let r(n) denote the number of integral ideals of norm n in a cubic extension K of the rationals, and define S(x) = ∑n≤x r(n) and (x) = S(x) - αx where α is the residue of the Dedekind zeta function ζ(s,K) at 1. It is shown that the abscissa of convergence of ∫0 (ey)2 e-2yσ dy is 1/3 as expected.

Original languageEnglish (US)
Pages (from-to)169-183
Number of pages15
JournalJournal of Number Theory
Volume100
Issue number1
DOIs
StatePublished - May 1 2003

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Dedekind zeta Function
Abscissa
Cubic Fields
Mean value theorem
Denote
Norm

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

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title = "A mean value theorem for cubic fields",
abstract = "Let r(n) denote the number of integral ideals of norm n in a cubic extension K of the rationals, and define S(x) = ∑n≤x r(n) and (x) = S(x) - αx where α is the residue of the Dedekind zeta function ζ(s,K) at 1. It is shown that the abscissa of convergence of ∫0∞ (ey)2 e-2yσ dy is 1/3 as expected.",
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A mean value theorem for cubic fields. / Vaughan, Robert Charles.

In: Journal of Number Theory, Vol. 100, No. 1, 01.05.2003, p. 169-183.

Research output: Contribution to journalArticle

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N2 - Let r(n) denote the number of integral ideals of norm n in a cubic extension K of the rationals, and define S(x) = ∑n≤x r(n) and (x) = S(x) - αx where α is the residue of the Dedekind zeta function ζ(s,K) at 1. It is shown that the abscissa of convergence of ∫0∞ (ey)2 e-2yσ dy is 1/3 as expected.

AB - Let r(n) denote the number of integral ideals of norm n in a cubic extension K of the rationals, and define S(x) = ∑n≤x r(n) and (x) = S(x) - αx where α is the residue of the Dedekind zeta function ζ(s,K) at 1. It is shown that the abscissa of convergence of ∫0∞ (ey)2 e-2yσ dy is 1/3 as expected.

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