Geodesic
EXPLICIT REPRESENTATIONS OF THE INTEGRAL CONTAINING THE ERROR TERM IN THE DIVISOR PROBLEM II
Glasgow mathematical journal, Tome 54 (2012) no. 1, pp. 133-147

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.1017/S0017089511000474
Mots-clés : 11N37 
FURUYA, JUN; TANIGAWA, YOSHIO. EXPLICIT REPRESENTATIONS OF THE INTEGRAL CONTAINING THE ERROR TERM IN THE DIVISOR PROBLEM II. Glasgow mathematical journal, Tome 54 (2012) no. 1, pp. 133-147. doi: 10.1017/S0017089511000474
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