International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 64, Pages 4025-4031

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

Received 1 March 2003; Revised 9 May 2003

Copyright © 2003 E. P. Balanzario and E. Marmolejo-Olea. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.