In this paper we study the distribution in the arithmetic progressions (modulo a product of tqo primes) of reducible quadratic polynomials (an+b)(cn+d) in short intervals, i.e. when n ∈[x,x+H],H=o(x); here H=xϑ with φ∈]3/4,1[. Using Large Sieve techniques we get results beyond the classical level ϑ, reaching 3ϑ-3/2; these also improve the results of Salerno and Vitolo in “large” intervlas (ϑ=1) obtaining level 3/2 instead of 4/3.
ON THE DISTRIBUTION IN THE ARITHMETIC PROGRESSIONS OF REDUCIBLE QUADRATIC POLYNOMIALS IN SHORT INTERVALS
COPPOLA, Giovanni;SALERNO, Saverio
2000-01-01
Abstract
In this paper we study the distribution in the arithmetic progressions (modulo a product of tqo primes) of reducible quadratic polynomials (an+b)(cn+d) in short intervals, i.e. when n ∈[x,x+H],H=o(x); here H=xϑ with φ∈]3/4,1[. Using Large Sieve techniques we get results beyond the classical level ϑ, reaching 3ϑ-3/2; these also improve the results of Salerno and Vitolo in “large” intervlas (ϑ=1) obtaining level 3/2 instead of 4/3.File in questo prodotto:
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