Purpose In this paper, the authors take first step in study of constructive methods by using Sobolev polynomials. Design/methodology/approach To do that, use connection formulas between polynomials and classical Laguerre polynomials, as well well-known Fourier coefficients for these latter. Findings Then, compute explicit some families Laguerre–Sobolev type orthogonal over a finite interval. Th...

The Fourier coefficients of modular forms encode very interesting arithmetic data. For example, divisor sums, partition numbers, trace of Frobenius of the reduction modulo primes of an elliptic curve over Q, and more generally, trace of Frobenius of many Galois representations of dimension 2 over finite fields (this being a conjecture of Serre) are all known to be, or conjectured to be, Fourier...