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On the distribution in the arithmetic progressions of reducible quadratic polynomials in short intervals, II

Giovanni CoppolaSaverio Salerno — 2001

Journal de théorie des nombres de Bordeaux

This paper gives further results about the distribution in the arithmetic progressions (modulo a product of two primes) of reducible quadratic polynomials ( a n + b ) ( c n + d ) in short intervals n [ x , x + x ϑ ] , where now ϑ ( 0 , 1 ] . Here we use the Dispersion Method instead of the Large Sieve to get results beyond the classical level ϑ , reaching 3 ϑ / 2 (thus improving also the level of the previous paper, i.e. 3 ϑ - 3 / 2 ), but our new results are different in structure. Then, we make a graphical comparison of the two methods.

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