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EXPLICIT REPRESENTATIONS OF THE INTEGRAL CONTAINING THE ERROR TERM IN THE DIVISOR PROBLEM II
- Source :
- Glasgow Mathematical Journal. 54:133-147
- Publication Year :
- 2011
- Publisher :
- Cambridge University Press (CUP), 2011.
-
Abstract
- In our previous paper [2], we derived an explicit representation of the integral ∫1∞t−θΔ(t)logjtdt by differentiation under the integral sign. Here, j is a fixed natural number, θ is a complex number with 1 < θ ≤ 5/4 and Δ(x) denotes the error term in the Dirichlet divisor problem. In this paper, we shall reconsider the same formula by an alternative approach, which appeals to only the elementary integral formulas concerning the Riemann zeta- and periodic Bernoulli functions. We also study the corresponding formula in the case of the circle problem of Gauss.
Details
- ISSN :
- 1469509X and 00170895
- Volume :
- 54
- Database :
- OpenAIRE
- Journal :
- Glasgow Mathematical Journal
- Accession number :
- edsair.doi...........374c8a4349cbd5aad54c5d6d1ddc6e58