Recovering Fourier Coefficients of Some Functions and Factorization of Integer Numbers / *Preobrazhenskii S.N.* // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2010. № 4. P. 40-43
[Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 166-171].

It is shown that if a function
determined on the segment [-1, 1] has a sufficiently
good approximation by partial sums of its expansion over Legendre polynomial,
then, given the function's Fourier coefficients *c _{n}* for some subset of

*n*∈[

*n*

_{1},

*n*

_{2}], one can approximately recover them for all

*n*∈[

*n*

_{1},

*n*

_{2}]. A new approach to factorization of integer numbers is given as an application.

*Key words*:
computational number theory, complexity of computing,
algorithm, factorization, factoring of integers,
elliptic curves, modular forms, Fourier coefficients,
Legendre polynomials.