We study the mean-square (over x 2 [N, 2N]) of the ”symmetry sum” of arithmetical functions f, namely P |n−x|h sgn(n−x)f(n); in this way we are checking the symmetry of f in ”almost all” short intervals by elementary methods; actually, we use the Large Sieve alone, together with elementary considerations.
On the Simmetry of arithmetical functions in almost all short intervals
COPPOLA, Giovanni;SALERNO, Saverio
2004
Abstract
We study the mean-square (over x 2 [N, 2N]) of the ”symmetry sum” of arithmetical functions f, namely P |n−x|h sgn(n−x)f(n); in this way we are checking the symmetry of f in ”almost all” short intervals by elementary methods; actually, we use the Large Sieve alone, together with elementary considerations.File in questo prodotto:
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