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http -> https (the question was bumped anyway)
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Martin Sleziak
Martin Sleziak
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Concerning the question of a reference for maximizing $k$:

A polynomial with all coefficients $\pm1$ is called a Littlewood polynomial, see, e.g., http://en.wikipedia.org/wiki/Littlewood_polynomialhttps://en.wikipedia.org/wiki/Littlewood_polynomial. The question of Littlewood polynomials vanishing to high order at $x=1$ is in the literature. See, e.g., Daniel Berend and Shahar Golan, Littlewood polynomials with high order zeros, Math Comp 75 (2006) 1541-1552, freely available at http://www.ams.org/journals/mcom/2006-75-255/S0025-5718-06-01848-5/S0025-5718-06-01848-5.pdfhttps://www.ams.org/journals/mcom/2006-75-255/S0025-5718-06-01848-5/S0025-5718-06-01848-5.pdf Executive summary; some numbers are known, some bounds are known, much remains to be done.

Concerning the question of a reference for maximizing $k$:

A polynomial with all coefficients $\pm1$ is called a Littlewood polynomial, see, e.g., http://en.wikipedia.org/wiki/Littlewood_polynomial. The question of Littlewood polynomials vanishing to high order at $x=1$ is in the literature. See, e.g., Daniel Berend and Shahar Golan, Littlewood polynomials with high order zeros, Math Comp 75 (2006) 1541-1552, freely available at http://www.ams.org/journals/mcom/2006-75-255/S0025-5718-06-01848-5/S0025-5718-06-01848-5.pdf Executive summary; some numbers are known, some bounds are known, much remains to be done.

Concerning the question of a reference for maximizing $k$:

A polynomial with all coefficients $\pm1$ is called a Littlewood polynomial, see, e.g., https://en.wikipedia.org/wiki/Littlewood_polynomial. The question of Littlewood polynomials vanishing to high order at $x=1$ is in the literature. See, e.g., Daniel Berend and Shahar Golan, Littlewood polynomials with high order zeros, Math Comp 75 (2006) 1541-1552, freely available at https://www.ams.org/journals/mcom/2006-75-255/S0025-5718-06-01848-5/S0025-5718-06-01848-5.pdf Executive summary; some numbers are known, some bounds are known, much remains to be done.

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Gerry Myerson
Gerry Myerson
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Concerning the question of a reference for maximizing $k$:

A polynomial with all coefficients $\pm1$ is called a Littlewood polynomial, see, e.g., http://en.wikipedia.org/wiki/Littlewood_polynomial. The question of Littlewood polynomials vanishing to high order at $x=1$ is in the literature. See, e.g., Daniel Berend and Shahar Golan, Littlewood polynomials with high order zeros, Math Comp 75 (2006) 1541-1552, freely available at http://www.ams.org/journals/mcom/2006-75-255/S0025-5718-06-01848-5/S0025-5718-06-01848-5.pdf Executive summary; some numbers are known, some bounds are known, much remains to be done.

A polynomial with all coefficients $\pm1$ is called a Littlewood polynomial, see, e.g., http://en.wikipedia.org/wiki/Littlewood_polynomial. The question of Littlewood polynomials vanishing to high order at $x=1$ is in the literature. See, e.g., Daniel Berend and Shahar Golan, Littlewood polynomials with high order zeros, Math Comp 75 (2006) 1541-1552, freely available at http://www.ams.org/journals/mcom/2006-75-255/S0025-5718-06-01848-5/S0025-5718-06-01848-5.pdf Executive summary; some numbers are known, some bounds are known, much remains to be done.

Concerning the question of a reference for maximizing $k$:

A polynomial with all coefficients $\pm1$ is called a Littlewood polynomial, see, e.g., http://en.wikipedia.org/wiki/Littlewood_polynomial. The question of Littlewood polynomials vanishing to high order at $x=1$ is in the literature. See, e.g., Daniel Berend and Shahar Golan, Littlewood polynomials with high order zeros, Math Comp 75 (2006) 1541-1552, freely available at http://www.ams.org/journals/mcom/2006-75-255/S0025-5718-06-01848-5/S0025-5718-06-01848-5.pdf Executive summary; some numbers are known, some bounds are known, much remains to be done.

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Gerry Myerson
Gerry Myerson
  • 39.9k
  • 10
  • 186
  • 247

A polynomial with all coefficients $\pm1$ is called a Littlewood polynomial, see, e.g., http://en.wikipedia.org/wiki/Littlewood_polynomial. The question of Littlewood polynomials vanishing to high order at $x=1$ is in the literature. See, e.g., Daniel Berend and Shahar Golan, Littlewood polynomials with high order zeros, Math Comp 75 (2006) 1541-1552, freely available at http://www.ams.org/journals/mcom/2006-75-255/S0025-5718-06-01848-5/S0025-5718-06-01848-5.pdf Executive summary; some numbers are known, some bounds are known, much remains to be done.