International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 23, Pages 3767-3780

Analytic Erdös-Turán conjectures and Erdös-Fuchs theorem

L. Haddad,1 C. Helou,2 and J. Pihko3

1120 rue de Charonne, Paris 75011, France
2Department of Mathematics, Penn State University, 25 Yearsley Mill Road, Media 19063, PA, USA
3Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68 (G. Hallstromin katu 2b), FI-00014, Finland

Received 3 March 2005; Revised 28 September 2005

Copyright © 2005 L. Haddad et al. 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 consider and study formal power series, that we call supported series, with real coefficients which are either zero or bounded below by some positive constant. The sequences of such coefficients have a lot of similarity with sequences of natural numbers considered in additive number theory. It is this analogy that we pursue, thus establishing many properties and giving equivalent statements to the well-known Erdös-Turán conjectures in terms of supported series and extending to them a version of Erdös-Fuchs theorem.