Long and Short Sums of a Twisted Divisor Function
2, allée de la Combe
be a prime number and define
is the number of divisors of
is the Legendre symbol. When
is a quadratic residue modulo
, then the convolution
could be close to the
number of divisors of
. The aim of this work is to compare the mean
value of the function
to the well known
average order of
. A bound for short sums in the case
also given, using profound results from the theory of integer points
close to certain smooth curves.
Full version: pdf,
(Concerned with sequences
Received January 14 2017; revised versions received June 1 2017; June 26 2017.
Published in Journal of Integer Sequences, July 1 2017.
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