Geodesic
Recovering fourier coefficients of some functions and factorization of integer numbers
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2010), pp. 33-39
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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 can approximately recover them for all $n\in[n_1,n_2]$. As an application, a new approach to factoring of integers is given. 
@article{VMUMM_2010_4_a5,
     author = {S. N. Preobrazhenskii},
     title = {Recovering fourier coefficients of some functions and factorization of integer numbers},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {33--39},
     year = {2010},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2010_4_a5/}
}
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S. N. Preobrazhenskii. Recovering fourier coefficients of some functions and factorization of integer numbers. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2010), pp. 33-39. http://geodesic.mathdoc.fr/item/VMUMM_2010_4_a5/