Corpus ID: 118837651

# On the Symmetry Integral

@article{Coppola2010OnTS,
title={On the Symmetry Integral},
author={G. Coppola},
journal={arXiv: Number Theory},
year={2010}
}
• G. Coppola
• Published 2010
• Mathematics
• arXiv: Number Theory
• We give a level one result for the "symmetry integral", say $I_f(N,h)$, of essentially bounded $f:\N \to \R$; i.e., we get a kind of "square-root cancellation" \thinspace bound for the mean-square (in $N 0$ we have $g(n)\ll_{\epsilon} n^{\epsilon}$, and supported in $[1,Q]$, with $Q\ll N$ (so, the exponent of $Q$ relative to $N$, say the level $\lambda:=(\log Q)/(\log N)$ is $\lambda < 1$), where the symmetry sum weights the $f-$values in (almost all, i.e. all but $o(N)$ possible exceptions… CONTINUE READING
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