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Izv. RAN. Ser. Mat., 2013, Volume 77, Issue 5, Pages 71–94 (Mi izv7990)  

On new results related to Gram's law

M. A. Korolevab

a Steklov Mathematical Institute, Russian Academy of Sciences
b National Engineering Physics Institute "MEPhI", Moscow

Abstract: We prove a number of new results related to Gram's law in the theory of the Riemann zeta-function that reflect irregularity in the distribution of the ordinates of the complex zeros of that function. Results are obtained on the distribution of pairs, triples, quadruples, … of adjacent ordinates of such zeros that simultaneously do not obey Gram's law.

Keywords: Riemann zeta-function, Gram's law, Gram's rule.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00759-a


DOI: https://doi.org/10.4213/im7990

Full text: PDF file (580 kB)
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English version:
Izvestiya: Mathematics, 2013, 77:5, 917–940

Bibliographic databases:

UDC: 511.331
MSC: 11M26, 11M06
Received: 12.04.2012

Citation: M. A. Korolev, “On new results related to Gram's law”, Izv. RAN. Ser. Mat., 77:5 (2013), 71–94; Izv. Math., 77:5 (2013), 917–940

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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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