TY - JOUR
T1 - Analytic Erdös-Turán conjectures and Erdös-Fuchs theorem
AU - Haddad, L.
AU - Helou, C.
AU - Pihko, J.
PY - 2005
Y1 - 2005
N2 - 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 Erdós-Fuchs theorem.
AB - 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 Erdós-Fuchs theorem.
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U2 - 10.1155/IJMMS.2005.3767
DO - 10.1155/IJMMS.2005.3767
M3 - Article
AN - SCOPUS:33746695996
SN - 0161-1712
VL - 2005
SP - 3767
EP - 3780
JO - International Journal of Mathematics and Mathematical Sciences
JF - International Journal of Mathematics and Mathematical Sciences
IS - 23
ER -