Wyniki wyszukiwania

1

Jumps of ternary cyclotomic coefficients

100%

Bzdęga B.

Acta Arithmetica

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2014

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tom 163

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nr 3

203-213

EN

It is known that two consecutive coefficients of a ternary cyclotomic polynomial $Φ_{pqr}(x)= ∑_k a_{pqr}(k)x^k$ differ by at most one. We characterize all k such that $|a_{pqr}(k)-a_{pqr}(k-1)|=1$. We use this to prove that the number of nonzero coefficients of the nth ternary cyclotomic polynomial is greater than $n^{1/3}$.

2

On a generalization of the Beiter Conjecture

100%

Bzdęga B.

Acta Arithmetica

|

2016

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tom 173

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nr 2

133-140

EN

We prove that for every ε > 0 and every nonnegative integer w there exist primes $p_1,...,p_w$ such that for $n = p_1... p_w$ the height of the cyclotomic polynomial $Φ_n$ is at least $(1-ε) c_w M_n$, where $M_n = ∏_{i=1}^{w-2} p_i^{2^{w-1-i}-1}$ and $c_w$ is a constant depending only on w; furthermore $lim_{w→∞} c_w^{2^{-w}} ≈ 0.71$. In our construction we can have $p_i > h(p_1... p_{i-1})$ for all i = 1,...,w and any function h: ℝ₊ → ℝ₊.

3

Bounds on ternary cyclotomic coefficients

75%

Bzdęga B.

Acta Arithmetica

|

2010

|

tom 144

|

nr 1

5-16

4

On the height of cyclotomic polynomials

75%

Bzdęga B.

Acta Arithmetica

|

2012

|

tom 152

|

nr 4

349-359

Ograniczanie wyników

4 Acta Arithmetica

4 Bzdęga B.

1 2016

1 2014

1 2012

1 2010

Jumps of ternary cyclotomic coefficients

On a generalization of the Beiter Conjecture

Bounds on ternary cyclotomic coefficients

On the height of cyclotomic polynomials