On the lattice of polynomials with integer coefficients: successive minima in $L_2(0,1)$

Abstract

. Let P Z n be the additive subgroup of the real Hilbert space L 2 (0 , 1) consisting of polynomials of order ≤ n with integer coefficients. We may treat P Z n as a lattice in ( n + 1) -dimensional Euclidean space; let λ i ( P Z n ) ( 1 ≤ i ≤ n + 1 ) be the corresponding successive minima. We give rather precise estimates of λ i ( P Z n ) for i (cid:38) 23 n .