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Moree, Pieter
- Neighboring Ternary Cyclotomic Coefficients Differ by at Most One
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As an application we reprove in a simpler way a result of Bachman from 2004 on ternary cyclotomic polynomials with an optimally large set of coefficients.
Authors
Yves Gallot
1,
Pieter Moree
2
Affiliations
1 I2 Bis Rue Perrey, 31400 Toulouse, FR
2 Max-Planck-Institut Fur Mathematik, Vivatsgasse 7, D-53111 Bonn, DE
1 I2 Bis Rue Perrey, 31400 Toulouse, FR
2 Max-Planck-Institut Fur Mathematik, Vivatsgasse 7, D-53111 Bonn, DE
Source
Journal of the Ramanujan Mathematical Society, Vol 24, No 3 (2009), Pagination: 235-248Abstract
A cyclotomic polynomial Φn(x) is said to be ternary if n=pqr with p, q and r distinct odd prime factors. Ternary cyclotomic polynomials are the simplest ones for which the behaviour of the coefficients is not completely understood. Eli Leher showed in 2007 that neighboring ternary cyclotomic coefficients differ by at most four. We show that, in fact, they differ by at most one. Consequently, the set of coefficients occurring in a ternary cyclotomic polynomial consists of consecutive integers.As an application we reprove in a simpler way a result of Bachman from 2004 on ternary cyclotomic polynomials with an optimally large set of coefficients.
- Counting Terms Un of Third Order Linear Recurrences with Un = U2 + nv2
Abstract Views :190 |
PDF Views:1
Authors
Affiliations
1 Rheinische Friedrich-Wilhelms-Universitat Bonn, Regina Pacis Weg 3, D-53113 Bonn, DE
2 School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, ZA
3 Max Planck Institut fur Mathematik, Vivatsgasse 7, D-53111 Bonn, DE
1 Rheinische Friedrich-Wilhelms-Universitat Bonn, Regina Pacis Weg 3, D-53113 Bonn, DE
2 School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, ZA
3 Max Planck Institut fur Mathematik, Vivatsgasse 7, D-53111 Bonn, DE