Let be a prime number and define where is the number of divisors of and 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 is also given, using profound results from the theory of integer points close to certain smooth curves.
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