Fujii's development on Chebyshev's conjecture

David J Platt; Timothy Trudgian

doi:10.1142/S1793042119500337

Fujii's development on Chebyshev's conjecture

David J Platt, Timothy Trudgian

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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Abstract

Chebyshev presented a conjecture after observing the apparent bias towards primes congruent to 3(mod 4). His conjecture is equivalent to a version of the Generalized Riemann Hypothesis. Fujii strengthened this conjecture; we strengthen it still further using detailed computations of zeroes of Dirichlet L-functions.

Original language	English
Pages (from-to)	639-644
Number of pages	6
Journal	International Journal of Number Theory
Volume	15
Issue number	3
Early online date	16 Nov 2018
DOIs	https://doi.org/10.1142/S1793042119500337
Publication status	Published - 1 Apr 2019

Keywords

Chebyshev bias
Dirichlet L-functions
Generalized Riemann Hypothesis

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10.1142/S1793042119500337

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This is the accepted author manuscript (AAM). The final published version (version of record) is available online via World Scientific at https://doi.org/10.1142/S1793042119500337 . Please refer to any applicable terms of use of the publisher.
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https://arxiv.org/abs/1802.00089Licence: Unspecified

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title = "Fujii's development on Chebyshev's conjecture",

abstract = "Chebyshev presented a conjecture after observing the apparent bias towards primes congruent to 3(mod 4). His conjecture is equivalent to a version of the Generalized Riemann Hypothesis. Fujii strengthened this conjecture; we strengthen it still further using detailed computations of zeroes of Dirichlet L-functions.",

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AU - Platt, David J

AU - Trudgian, Timothy

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AB - Chebyshev presented a conjecture after observing the apparent bias towards primes congruent to 3(mod 4). His conjecture is equivalent to a version of the Generalized Riemann Hypothesis. Fujii strengthened this conjecture; we strengthen it still further using detailed computations of zeroes of Dirichlet L-functions.

KW - Chebyshev bias

KW - Dirichlet L-functions

KW - Generalized Riemann Hypothesis

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M3 - Article (Academic Journal)

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EP - 644

JO - International Journal of Number Theory

JF - International Journal of Number Theory

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ER -

Fujii's development on Chebyshev's conjecture

Abstract

Keywords

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Fujii's development on Chebyshev's conjecture

Abstract

Keywords

Access to Document

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HPC (High Performance Computing) and HTC (High Throughput Computing) Facilities

Cite this