Large values of certain number-theoretic error terms

Aleksandar Ivić

Displaying similar documents to “Large values of certain number-theoretic error terms”

An alternative approach to a theorem of Tom Meurman

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J. Proschan (1971)

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K. Chandrasekharan, H. Joris (1973)

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A generalization of Atkinson's formula to L-functions

Tom Meurman (1986)

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Piotr Zarzycki (1989)

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Chang-Pao Chen (1994)

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We prove that if $c_{j k} \to 0$ as max(|j|,|k|) → ∞, and $\sum_{| j | = 0 \pm}^{\infty} \sum_{| k | = 0 \pm}^{\infty} {θ (| j |}^{⊤} {) ϑ (| k |}^{⊤}) | Δ_{12} c_{j k} | < \infty$ , then f(x,y)ϕ(x)ψ(y) ∈ L¹(T²) and $\iint_{T ²} | s_{m n} (x, y) - f (x, y) | \cdot | ϕ (x) ψ (y) | d x d y \to 0$ as min(m,n) → ∞, where f(x,y) is the limiting function of the rectangular partial sums $s_{m n} (x, y)$ , (ϕ,θ) and (ψ,ϑ) are pairs of type I. A generalization of this result concerning L¹-convergence is also established. Extensions of these results to double series of orthogonal functions are also considered. These results can be extended to n-dimensional case. The aforementioned results generalize work of Balashov [1],...

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J. Loxton (1984)

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B. Srinivasan (1963)

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