Recovering Fourier coefficients of modular forms and factoring of integers

Details Recovering Fourier coefficients of modular forms and factoring of integers Recovering Fourier coefficients of modular forms and factoring of integers

2010-08-30

arxiv.org/abs/1008.5035v1

Mathematics

Number Theory

8 pages

Scientific paper

It is shown that if a function defined on the segment [-1,1] has sufficiently
good approximation by partial sums of the Legendre polynomial expansion, then,
given the function's Fourier coefficients $c_n$ for some subset of
$n\in[n_1,n_2]$, one may approximately recover them for all $n\in[n_1,n_2]$. As
an application, a new approach to factoring of integers is given.

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