Generalized Bombieri–Lagarias’ theorem and generalized Li’s criterion with its arithmetic interpretation

• Published in: Український математичний журнал
• Date: 2014
• ISSN: 1027-3190
• Main Author: Sekatski, S.K.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2014
• Subjects: Статті
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/165313
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Generalized Bombieri–Lagarias’ theorem and generalized Li’s criterion with its arithmetic interpretation / S.K. Sekatski // Український математичний журнал. — 2014. — Т. 66, № 3. — С. 371–383. — Бібліогр.: 13 назв. — англ.

We show that Li’s criterion equivalent to the Riemann hypothesis, i.e., the statement that the sums kn=Σρ(1−(1−1ρ)n) over zeros of the Riemann xi-function and the derivatives are nonnegative if and only if the Riemann hypothesis is true, can be generalized and the nonnegativity of certain derivative...