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ON THE VALUE DISTRIBUTION OF TWO DIRICHLET L-FUNCTIONS
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
UCL, Dept Math, Gower St, London WC1E 6BT, England..
2018 (English)In: FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, ISSN 0208-6573, Vol. 58, no 1, p. 43-68Article in journal (Refereed) Published
Abstract [en]

Let rho denote the non-trivial zeros of the Riemann zeta function. We study the relative value distribution of L(rho + sigma, chi(1)) and L(rho + sigma, chi(2)), where sigma is an element of[0, 1/2) is fixed and chi(1), chi(2) are two fixed Dirichlet characters to distinct prime moduli. For sigma > 0 we prove that a positive proportion of these pairs of values are linearly independent over R, which implies that the arguments of the values are different. For sigma = 0 we show that, up to height T, the values are different for cT of the Riemann zeros for some positive constant c.

Place, publisher, year, edition, pages
WYDAWNICTWO NAUKOWE UAM , 2018. Vol. 58, no 1, p. 43-68
Keywords [en]
Dirichlet L-function, value-distribution
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-226225DOI: 10.7169/facm/1640ISI: 000428216400004OAI: oai:DiVA.org:kth-226225DiVA, id: diva2:1211567
Note

QC 20180531

Available from: 2018-05-31 Created: 2018-05-31 Last updated: 2018-05-31Bibliographically approved

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Laaksonen, Niko

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