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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 cn 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.
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