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A certain continuity property of the res...

Shinya, Hisanobu...

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A certain continuity property of the residues of the poles of ∑n≥1Λ(n)e−2πiqnn−s with respect to q∈Q∩(0,1) and the Riemann hypothesis by Shinya, Hisanobu ( Author )

Content Provider	Lemonjar Open Access
Publisher	N.A
Publication Date	04-06-2007
Summary	The purpose of this article is to present some result which may characterize nontrivial zeros of the Riemann zeta-function off the critical line Re(s)=1/2, if any exists. In brief, it concerns the residues of the poles of the function M(s,q)≡∑n≥1Λ(n)e−2πiqnn−s, where Λ is the arithmetical Mangoldt Λ-function. Suppose that M(s,1/2) has a pole for some complex number ρ∗, with Re(ρ∗)>1/2. Then we discuss a certain continuity property of the residues of the poles of M(ρ∗,q) with respect to the variable q∈Q∩(1/2,1).
ISBN	-
Item Type	Article
File Type	pdf
File Size	36.88 KB
Language	English
Subjects	-
Unlimited	MYR 0.00
Total read	-
URL	http://arxiv.org/abs/0706.0357

Citation

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AMA 11th EditionReferences

Shinya, Hisanobu. A certain continuity property of the residues of the poles of ∑n≥1Λ(n)e−2πiqnn−s with respect to q∈Q∩(0,1) and the Riemann hypothesis. N.A. June 04, 2007. Accessed August 24, 2025. https://online.provdatabase.com/cite/12604

APA 7th EditionReferences

Shinya, Hisanobu. (2007). A certain continuity property of the residues of the poles of ∑n≥1Λ(n)e−2πiqnn−s with respect to q∈Q∩(0,1) and the Riemann hypothesis. N.A. https://online.provdatabase.com/cite/12604

Chicago 17th EditionReferences

Shinya, Hisanobu. A certain continuity property of the residues of the poles of ∑n≥1Λ(n)e−2πiqnn−s with respect to q∈Q∩(0,1) and the Riemann hypothesis. N.A. 2007. https://online.provdatabase.com/cite/12604

HarvardReferences

Shinya, Hisanobu. (2007). A certain continuity property of the residues of the poles of ∑n≥1Λ(n)e−2πiqnn−s with respect to q∈Q∩(0,1) and the Riemann hypothesis. [Online]. N.A. Available from: https://online.provdatabase.com/cite/12604. (Accessed 24 August 2025).

Harvard AustraliaReferences

Shinya, Hisanobu, 2007, A certain continuity property of the residues of the poles of ∑n≥1Λ(n)e−2πiqnn−s with respect to q∈Q∩(0,1) and the Riemann hypothesis, N.A, viewed 24 August 2025, <https://online.provdatabase.com/cite/12604>

MLA 9th EditionWorks Cited

Shinya, Hisanobu. A certain continuity property of the residues of the poles of ∑n≥1Λ(n)e−2πiqnn−s with respect to q∈Q∩(0,1) and the Riemann hypothesis. N.A, 2007. PROV Database, https://online.provdatabase.com/cite/12604.

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