The number of factorizations of numbers less than x x into factors less than y y Academic Article uri icon

abstract

  • Let K ( x , y ) K(x,y) be the number in the title. There is a function f ( r ) f(r) , concave and decreasing with f ( 0 ) = 2 f(0) = 2 and f ( 0 ) = 0 f(0) = 0 such that if r = log x / log y r = sqrt {log x} /log y then as x x o infty with r r fixed, [ K ( x , y ) = x exp ( f ( r ) log x + O ( log log x ) 2 ) K(x,y) = x exp ,left ({f(r),sqrt {log x} + O,{{(log log x)}^2}}
    ight )
    ]
    . The proof uses a uniform version of Chernoffs theorem on large deviations from the sample mean of a sum of N N

published proceedings

  • Transactions of the American Mathematical Society

author list (cited authors)

  • Hensley, D.

citation count

  • 2

complete list of authors

  • Hensley, Douglas

publication date

  • January 1983