On some mean value results for the zeta-function in short intervals

• Autorzy: Aleksandar Ivić
• Języki publikacji: EN

Abstrakty

EN

Let $Δ(x)$ denote the error term in the Dirichlet divisor problem, and let E(T) denote the error term in the asymptotic formula for the mean square of |ζ(1/2+it)|. If E*(t) := E(t) - 2πΔ*(t/(2π)) with Δ*(x) = -Δ(x) + 2Δ(2x) - 1/2Δ(4x) and $∫_0^T E*(t) dt = 3/4πT + R(T)$, then we obtain a number of results involving the moments of |ζ(1/2+it)| in short intervals, by connecting them to the moments of E*(T) and R(T) in short intervals. Upper bounds and asymptotic formulae for integrals of the form
∫_T^{2T}(∫_{t-H}^{t+H} |ζ(1/2+iu|^2 du}^k dt$ (k ∈ ℕ, 1 ≪ H ≤ T)
are also treated.

Kategorie tematyczne

• 11N37: Asymptotic results on arithmetic functions
• 11M06: ζ ( s ) and L ( s , χ )

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 162
• Numer: 2
• Strony: 141-158

Daty

wydano

2014

Twórcy

autor

Aleksandar Ivić

• Katedra Matematike RGF-a, Universiteta u Beogradu, Dušina 7, 11000 Beograd, Serbia

Identyfikatory

DOI

10.4064/aa162-2-2