Jacobi's four-square theorem

28 year-old Painting Investments Worker Truman from Regina, usually spends time with pastimes for instance interior design, property developers in new launch ec Singapore and writing. Last month just traveled to City of the Renaissance. In mathematics, a Littlewood polynomial is a polynomial all of whose coefficients are +1 or −1. Littlewood's problem asks how large the values of such a polynomial must be on the unit circle in the complex plane. The answer to this would yield information about the autocorrelation of binary sequences. They are named for J. E. Littlewood who studied them in the 1950s.

Definition

A polynomial

$p(x)=\sum _{i=0}^{n}a_{i}x^{i}\,$

is a Littlewood polynomial if all the $a_{i}=\pm 1$. Littlewood's problem asks for constants c₁ and c₂ such that there are infinitely many Littlewood polynomials p_n , of increasing degree n satisfying

$c_{1}{\sqrt {n+1}}\leq |p_{n}(z)|\leq c_{2}{\sqrt {n+1}}.\,$

for all $z$ on the unit circle. The Rudin-Shapiro polynomials provide a sequence satisfying the upper bound with $c_{2}={\sqrt {2}}$. No sequence is known (as of 2008) which satisfies the lower bound.

References

• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
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• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534