On equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis

By using the generalized Littlewood theorem about a contour integral involving the logarithm of an analytic function, we show how an infinite number of integral equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis can be established and present some of them as an example. It is shown that all earlier known equalities of this type, viz., the Wang equality, Volchkov equality, Balazard–Saias–Yor equality, and an equality established by one of the authors, are certain special cases of our general approach.Показано як за допомогою узагальненої теореми Лiттлвуда про контурний iнтеграл, що мiстить логарифм аналiтичної функцiї, можна отримати нескiнченну кiлькiсть iнтегральних рiвностей, що мiстять iнтеграли вiд логарифма ζ-функцiї Рiмана i є еквiвалентними гiпотезi Рiмана, i наведено кiлька таких рiвностей у якостi прикладу. Показано, що деякi вiдомi рiвностi такого типу, а саме, рiвностi Ванга, Волчкова, Балазарда – Сайаса – Йора та рiвнiсть, що встановлена одним iз авторiв, є частинними випадками нaшого загального пiдход

Structure of Nipah virus unassembled nucleoprotein in complex with its viral chaperone.

International audienceNipah virus (NiV) is a highly pathogenic emergent paramyxovirus causing deadly encephalitis in humans. Its replication requires a constant supply of unassembled nucleoprotein (N(0)) in complex with its viral chaperone, the phosphoprotein (P). To elucidate the chaperone function of P, we reconstituted NiV the N(0)-P core complex and determined its crystal structure. The binding of the N-terminal region of P blocks the polymerization of N by interfering with subdomain exchange between N protomers and keeps N(0) in an open conformation, ready to grasp an RNA molecule. We found that a peptide derived from the N-binding region of P protects cells against viral infection and demonstrated by structure-based mutagenesis that this peptide acts by inhibiting N(0)-P formation. These results provide new insights about the assembly of N along genomic RNA and validate the N(0)-P complex as a target for drug development