On the Symmetry of Divisor Sums Functions in Almost All Short Intervals
نویسنده
چکیده
We study the symmetry of divisor sums functions σ−s(n) def = ∑ d|n d −s (for σ = Re(s) > 0) in almost all short intervals; by elementary methods (based on the Large Sieve) we give an exact asymptotic estimate for the mean-square (over N < x ≤ 2N) of their “symmetry sum” ∑ |n−x|≤h sgn(n− x)σ−s(n) (here sgn(0) = 0 and sgn(t) def = t/|t|, for t 6= 0).
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