Explicit merit factor formulae for Fekete and Turyn polynomials (Q2750951)
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scientific article; zbMATH DE number 1663194
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Explicit merit factor formulae for Fekete and Turyn polynomials |
scientific article; zbMATH DE number 1663194 |
Statements
Explicit merit factor formulae for Fekete and Turyn polynomials (English)
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21 October 2001
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class number
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\((-1,1)\)-coefficients
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merit factor
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Fekete polynomials
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Turyn polynomials
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Littlewood polynomials
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Explicit formulas are given for the \(L_4\) norm of various sequences of polynomials related to the Fekete polynomials \(f_q(z)= \sum^{q-1}_{k=1} ({k\over q})z^k\), where \(({k\over q})\) is a Legendre symbol and \(q\) is an odd prime. For example, \(\|f_q\|^4_4= {5q^2\over 3}-3q+ {4\over 3}-12 (h(-q))^2\), where \(h(-q)\) is the class number of \(\mathbb{Q}(\sqrt {-q})\).
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