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Inverse Cyclotomic Polynomials

Author: QianGang
Tutor: QinHouRong
School: Nanjing University
Course: Basic mathematics
Keywords: Cyclotomic polynomial Inverse cyclotomic polynomial Ternary flat inverse cyclotomic polynomial
CLC: O174.14
Type: Master's thesis
Year: 2011
Downloads: 9
Quote: 0
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Abstract


About cyclotomic polynomial φn (χ) coefficient has been more in-depth research , the n-th inverse cyclotomic polynomial Ψn ( χ ) = ( χn - 1 ) / φn (χ ) . We use C (n) represents the absolute value of the inverse n-th cyclotomic polynomial absolute value of the largest coefficient . Pieter Moree prove he inverse cyclotomic polynomial article C (pqr) ≤ (p-1), at the same time gives the necessary and sufficient conditions for equality . This article was first proved in the p, q, r is a prime number and meet QP 2 , r ≡ 1 ( mod p ) , under conditions , when in the case where C ( PQR ) ≤ 2 . An example is given at the same time prove that C ( pqr ) ≤ 2 equal sign established . Finally, we have to weaken the restriction of q prove when q ≡ 2 (mod p), r ≡ 1 (mod p), if the R GT ; then C ( PQR ) = 1 ;

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Theory of functions > Real Analysis,Real Variable > Polynomial theory
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