In this paper we study the symmetry of the divisor function in almost all short intervals. We use the Large Sieve to derive a bound for the divisor function, d(n) (number of divisors of n). This function has the useful property of “flipping”, which can be applied, more generally, when dealing with the symmetry of an arithmetical function f(n) which is the Dirichlet convolution of a (fixed) arithmetical function g(n) with itself. However, to apply our method, we also need the hypothesis that g is “smooth and with small derivative".
ON THE SYMMETRY OF THE DIVISOR FUNCTION IN ALMOST ALL SHORT INTERVALS
COPPOLA, Giovanni;SALERNO, Saverio
2004-01-01
Abstract
In this paper we study the symmetry of the divisor function in almost all short intervals. We use the Large Sieve to derive a bound for the divisor function, d(n) (number of divisors of n). This function has the useful property of “flipping”, which can be applied, more generally, when dealing with the symmetry of an arithmetical function f(n) which is the Dirichlet convolution of a (fixed) arithmetical function g(n) with itself. However, to apply our method, we also need the hypothesis that g is “smooth and with small derivative".File in questo prodotto:
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