Analytic Erdös-Turán conjectures and Erdös-Fuchs theorem
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...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.3767 |
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| author | L. Haddad C. Helou J. Pihko |
| author_facet | L. Haddad C. Helou J. Pihko |
| author_sort | L. Haddad |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3588b08a36c24cde87fa45655eae9b5c |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3588b08a36c24cde87fa45655eae9b5c2025-02-03T01:25:57ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005233767378010.1155/IJMMS.2005.3767Analytic Erdös-Turán conjectures and Erdös-Fuchs theoremL. Haddad0C. Helou1J. Pihko2120 rue de Charonne, Paris 75011, FranceDepartment of Mathematics, Penn State University, 25 Yearsley Mill Road, Media 19063, PA, USADepartment of Mathematics and Statistics, University of Helsinki, P.O. Box 68 (G. Hallstromin katu 2b), FI-00014, FinlandWe 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.http://dx.doi.org/10.1155/IJMMS.2005.3767 |
| spellingShingle | L. Haddad C. Helou J. Pihko Analytic Erdös-Turán conjectures and Erdös-Fuchs theorem International Journal of Mathematics and Mathematical Sciences |
| title | Analytic Erdös-Turán conjectures and Erdös-Fuchs theorem |
| title_full | Analytic Erdös-Turán conjectures and Erdös-Fuchs theorem |
| title_fullStr | Analytic Erdös-Turán conjectures and Erdös-Fuchs theorem |
| title_full_unstemmed | Analytic Erdös-Turán conjectures and Erdös-Fuchs theorem |
| title_short | Analytic Erdös-Turán conjectures and Erdös-Fuchs theorem |
| title_sort | analytic erdos turan conjectures and erdos fuchs theorem |
| url | http://dx.doi.org/10.1155/IJMMS.2005.3767 |
| work_keys_str_mv | AT lhaddad analyticerdosturanconjecturesanderdosfuchstheorem AT chelou analyticerdosturanconjecturesanderdosfuchstheorem AT jpihko analyticerdosturanconjecturesanderdosfuchstheorem |