Short interval results for k-free values of irreducible polynomials
نویسندگان
چکیده
منابع مشابه
SHORT INTERVAL RESULTS FOR k FREE VALUES OF IRREDUCIBLE POLYNOMIALS
Let k be an integer 2. Trifonov and the author (cf. [3],[4],[15]) have recently made improvements on the gap problem of nding an h = h(x) as small as possible such that for x su ciently large, every interval of the form (x; x + h] contains a k free number. Although, one expects such h to exist with h as small as c log x for some constant c (K. McCurley and A. Zaccagnini, independent private com...
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For a polynomial f(T ) ∈ Z[T ], the frequency with which the values f(n) are prime has been considered since at least the 18-th century. Euler observed, in a letter to Goldbach in 1752, that the sequence n + 1 has many prime values for 1 ≤ n ≤ 1500. Legendre assumed an arithmetic progression an+ b with (a, b) = 1 contains infinitely many primes in his work on the quadratic reciprocity law. Ther...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1993
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-64-3-249-270