Simultaneous Polynomial Approximations of the Lerch Function
Canadian journal of mathematics, Tome 61 (2009) no. 6, pp. 1341-1356
Voir la notice de l'article provenant de la source Cambridge
We construct bivariate polynomial approximations of the Lerch function that for certain specialisations of the variables and parameters turn out to be Hermite–Padé approximants either of the polylogarithms or of Hurwitz zeta functions. In the former case, we recover known results, while in the latter the results are new and generalise some recent works of Beukers and Prévost. Finally, we make a detailed comparison of our work with Beukers’. Such constructions are useful in the arithmetical study of the values of the Riemann zeta function at integer points and of the Kubota–Leopold $p$ -adic zeta function.
Rivoal, Tanguy. Simultaneous Polynomial Approximations of the Lerch Function. Canadian journal of mathematics, Tome 61 (2009) no. 6, pp. 1341-1356. doi: 10.4153/CJM-2009-063-6
@article{10_4153_CJM_2009_063_6,
author = {Rivoal, Tanguy},
title = {Simultaneous {Polynomial} {Approximations} of the {Lerch} {Function}},
journal = {Canadian journal of mathematics},
pages = {1341--1356},
year = {2009},
volume = {61},
number = {6},
doi = {10.4153/CJM-2009-063-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2009-063-6/}
}
TY - JOUR AU - Rivoal, Tanguy TI - Simultaneous Polynomial Approximations of the Lerch Function JO - Canadian journal of mathematics PY - 2009 SP - 1341 EP - 1356 VL - 61 IS - 6 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2009-063-6/ DO - 10.4153/CJM-2009-063-6 ID - 10_4153_CJM_2009_063_6 ER -
Cité par Sources :