Section: New Results
Keywords : polynomial approximation, minimax approximation, Chebyshev polynomials, automatic generation, floating-point arithmetic, polytopes, linear programming, modular function, modular invariant, Fourier coefficient, circle method, Hankel function.
Efficient Polynomial Approximation
In  , N. Brisebarre, J.-M. Muller and A. Tisserand provide a general and efficient method for finding the best polynomial approximation under constraints of form and size in bits of the coefficients. The method described in  is currently implemented in the C library MEPLib (cf. § 5.10 ).
The modular invariant jis an important function in number theory  . G. Philibert (LARAL, Saint-Étienne) and N. Brisebarre established in  precise upper and lower bounds for the Fourier coefficients of jm for all . These results improve on previously known results, especially those of Mahler  and Herrmann  .