OFFSET
0,1
COMMENTS
Chern and Vaaler's estimate of the number M(d,T) of integer polynomials of degree at most d, and of Mahler's measure at most T, is M(d,T) = V(d+1)*T^(d+1) + O(T^d) as T -> infinity, where d is fixed and V(d+1) is the volume of the d-th Chern-Vaaler star body, which is nonconvex and symmetric. For the "monic slice" of the star body, see A288756, A288757, A288758.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..80
S.-J. Chern and J.D. Vaaler, The distribution of values of Mahler's measure, J. Reine. Angew. Math., 540 (2001), 1-47.
A. Dubickas, Review of S.-J. Chern and J.D. Vaaler's "The distribution of values of Mahler's measure", Zentralblatt 0986.11017
Robert Grizzard and Joseph Gunther, Slicing the stars: counting algebraic numbers, integers, and units by degree and height, arXiv:1609.08720 [math.NT] 2016.
FORMULA
EXAMPLE
2, 4, 8, 128/9, 640/27, 8192/225, 1605632/30375, 536870912/7441875, 100663296/1071875, ...
MATHEMATICA
v[d_] := (e = Floor[(d - 1)/2]; 2^(d + 1) (d + 1)^e Product[(2 k)^(d - 2 k)/(2 k + 1)^(d + 1 - 2 k), {k, 1, e}]); Table[ Numerator[v[d]], {d, 0, 18}]
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Jonathan Sondow, May 26 2017
STATUS
approved