Recovering Fourier Coefficients of Some Functions and Factorization of Integer Numbers / Preobrazhenskii S.N. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2010. ? 4. P. 33-39 [Moscow Univ. Math. Bulletin. Vol. 65, No 4, 2010. 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∈[n₁, n₂], one can approximately recover them for all n∈[n₁, n₂]. 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.