A mean value result involving the fourth moment of |ζ(1/2+it)|

2003/05/31 by Aleksandar Ivic
Mathematics · #math.NT #msc:11M06

paper · pdf

published as Annales Univ. Sci. Budapest, Sect. Computatorica 23(2004), 47-58 · 9 pages, only TeX formatting corrected

arxiv created 2003/11/10 · arxiv updated 2009/11/30

Abstract

If (k,ℓ) is an exponent pair such that k+ℓ<1, then we have ∫₁^T|ζ(1/2+it)|⁴|ζ(σ+it)|²dt ≪_εT^1+ε (σ> min(5\over6,max(ℓ-k, 5k+ℓ\over4k+1)), while if (k,ℓ) is an exponent pair such that 3k+ℓ<1, then we have ∫₁^T|ζ(1/2+it)|⁴|ζ(σ+it)|⁴dt ≪_εT^1+ε (σ> 11k+ℓ+1\over8k+2).

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