### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 3767-3780 |

Number of pages | 14 |

Journal | International Journal of Mathematics and Mathematical Sciences |

Volume | 2005 |

Issue number | 23 |

DOIs | |

State | Published - 2005 |

### All Science Journal Classification (ASJC) codes

- Mathematics (miscellaneous)

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## Cite this

Haddad, L., Helou, C., & Pihko, J. (2005). Analytic Erdös-Turán conjectures and Erdös-Fuchs theorem.

*International Journal of Mathematics and Mathematical Sciences*,*2005*(23), 3767-3780. https://doi.org/10.1155/IJMMS.2005.3767