Power series approximations to Fekete polynomials

Jason Bell; Igor E. Shparlinski

doi:10.1016/j.jat.2017.07.002

Power series approximations to Fekete polynomials

Jason Bell, Igor E. Shparlinski^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We study how well Fekete polynomials F_p(X)=∑n=0p−1[Formula presented]Xⁿ∈Z[X]with the coefficients given by Legendre symbols modulo a prime p can be approximated by power series representing algebraic functions of a given degree. We also obtain some explicit results describing polynomial recurrence relations which are satisfied by the coefficients of such algebraic functions.

Original language	English
Pages (from-to)	132-142
Number of pages	11
Journal	Journal of Approximation Theory
Volume	222
DOIs	https://doi.org/10.1016/j.jat.2017.07.002
Publication status	Published - 1 Oct 2017
Externally published	Yes

Keywords

Algebraic function
Fekete polynomial
Legendre symbol
Polynomial recurrences

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10.1016/j.jat.2017.07.002

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abstract = "We study how well Fekete polynomials Fp(X)=∑n=0p−1[Formula presented]Xn∈Z[X]with the coefficients given by Legendre symbols modulo a prime p can be approximated by power series representing algebraic functions of a given degree. We also obtain some explicit results describing polynomial recurrence relations which are satisfied by the coefficients of such algebraic functions.",

keywords = "Algebraic function, Fekete polynomial, Legendre symbol, Polynomial recurrences",

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year = "2017",

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AU - Shparlinski, Igor E.

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AB - We study how well Fekete polynomials Fp(X)=∑n=0p−1[Formula presented]Xn∈Z[X]with the coefficients given by Legendre symbols modulo a prime p can be approximated by power series representing algebraic functions of a given degree. We also obtain some explicit results describing polynomial recurrence relations which are satisfied by the coefficients of such algebraic functions.

KW - Algebraic function

KW - Fekete polynomial

KW - Legendre symbol

KW - Polynomial recurrences

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DO - 10.1016/j.jat.2017.07.002

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SP - 132

EP - 142

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

ER -

Power series approximations to Fekete polynomials

Abstract

Keywords

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