International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 64, Pages 4025-4031
doi:10.1155/S0161171203303345
Ingham Tauberian theorem with an estimate for the error term
E. P. Balanzario1
and E. Marmolejo-Olea2
1Instituto de Matemáticas, Universidad Nacional Autónoma de México, Morelia, A.P. 61-3 (Xangari), Morelia 58089 , Michoacán, Mexico
2Instituto de Matemáticas, Universidad Nacional Autónoma de México, Cuernavaca, A.P. 273, Cuernavaca 62251, Morelos, Mexico
Abstract
We estimate the error term in the Ingham Tauberian theorem. This estimation of the error term is accomplished by considering an elementary proof of a weak form of Wiener's general Tauberian theorem and by using a zero-free region for the Riemann zeta function.