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Localised factorizations of integers

  • Autores: Dimitris Koukoulopoulos
  • Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 101, Nº 2, 2010, págs. 392-426
  • Idioma: inglés
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  • Resumen
    • We determine the order of magnitude of H(k+1)(x, y, 2y), the number of integers n  x that are divisible by a product d1 · . . . · dk with yi < di  2yi, when the numbers log y1, . . . , log yk have the same order of magnitude and k  2. This generalizes a result by Kevin Ford when k = 1. As a corollary of these bounds, we determine the number of elements up to multiplicative constants that appear in a (k + 1)-dimensional multiplication table as well as how many distinct sums of k + 1 Farey fractions there are modulo 1.


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