On large values of the Riemann zeta-function on short segments of the critical line

• Autorzy: Maxim A. Korolev
• Języki publikacji: EN

Abstrakty

EN

We obtain a series of new conditional lower bounds for the modulus and the argument of the Riemann zeta function on very short segments of the critical line, based on the Riemann hypothesis. In particular, we prove that for any large fixed constant A > 1 there exist(non-effective) constants T₀(A) > 0 and c₀(A) > 0 such that the maximum of |ζ (0.5+it)| on the interval (T-h,T+h) is greater than A for any T > T₀ and h = (1/π)lnlnln{T}+c₀.

Kategorie tematyczne

• 11M06: ζ ( s ) and L ( s , χ )

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 166
• Numer: 4
• Strony: 349-390

Daty

wydano

2014

Twórcy

autor

Maxim A. Korolev

• Steklov Mathematical Institute, Russian Academy of Sciences, Gubkin St., 8, 119991 Moscow, Russia
• National Research Nuclear University, MEPhI, (Moscow Engineering Physics Institute), Kashirskoye sh., 31, 115409 Moscow, Russia

Identyfikatory

DOI

10.4064/aa166-4-3