Average Mahler’s measure and L p L_p norms of Littlewood polynomials Academic Article uri icon

abstract

  • Littlewood polynomials are polynomials with each of their coefficients in the set { 1 , 1 } {-1,1} . We compute asymptotic formulas for the arithmetic mean values of the Mahler’s measure and the L p L_p norms of Littlewood polynomials of degree n 1 n-1 . We show that the arithmetic means of the Mahler’s measure and the L p L_p norms of Littlewood polynomials of degree n 1 n-1 are asymptotically e γ / 2 n e^{-gamma /2}sqrt {n} and Γ ( 1 + p / 2 ) 1 / p n Gamma (1+p/2)^{1/p}sqrt {n} , respectively, as n n grows large. Here γ gamma is Euler’s constant. We also compute asymptotic formulas for the power means M α M_{alpha } of the L p L_p norms of Littlewood polynomials of degree n 1

author list (cited authors)

  • Choi, S., & Erdélyi, T.

publication date

  • January 1, 2014 11:11 AM