On the Modified Selberg Integral

Details On the Modified Selberg Integral On the Modified Selberg Integral

2010-06-07

arxiv.org/abs/1006.1229v1

Mathematics

Number Theory

6 pages (Plain TeX)

Scientific paper

We give a kind of \lq \lq approximate majorant principle\rq \rq \thinspace result for the \lq \lq modified Selberg integral\rq \rq, say $\modSel_f(N,h)$, of essentially bounded $f:\N \rightarrow \R$ (i.e., bounded by arbitrary small powers); i.e., we get an upper bound, in terms of the modified Selberg integral of a related function $F$ (with $|f\ast \mu|\ll F\ast \mu$, in the supports intersection), getting a \lq \lq square-root cancellation\rq \rq \thinspace for the error-terms. Here $\modSel_f(N,h)$ is the mean-square (in $N

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