https://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/60939/1/0983-10.pdf

Algorithms forb-Functions, Restrictions, and Algebraic Local Cohomology Groups ofD-Modules

We associate to any convenient nondegenerate Laurent polynomial on the complex torus (C^*)^n a canonical Frobenius-Saito structure on the base space of its universal unfolding. According to the method of K. Saito (primitive forms) and of M. Saito (good basis of the Gauss-Manin system), the main problem, which is solved in this article, is the analysis of the Gauss-Manin system of the Laurent polynomial (or its universal unfolding) and of the corresponding Hodge theory.

Gauss-Manin systems, Brieskorn lattices and Frobenius structures (I)

/pdf/an-algorithm-of-computing-b-functions-rrmxjhapsr.pdf

An algorithm of computing $b$-functions

In this paper, we prove the rationality of Igusa's local zeta functions of semiquasihomogeneous polynomials with coefficients in a non-archimedean local field K. The proof of this result is based on Igusa's stationary phase formula and some ideas on Neron p-desingularization.

/pdf/igusa-s-local-zeta-functions-of-semiquasihomogeneous-1mbj6vjls9.pdf

Igusa’s local zeta functions of semiquasihomogeneous polynomials

Les zéros de b sont rationnels : ceci est démontré par B. Malgrange, pour / à singularité isolée dans [19], en mettant en évidence un lien avec la monodromie de / (les valeurs propres de la monodromie sont les g-2î7i-û^ ^^ ^ Q^ ̂ p^p Kashiwara [11] dans le cas général en utilisant la résolution des singularités. Malgrange généralise ensuite son résultat aux singularités non isolées dans [20], Varchenko [26] interprète les zéros de & à l'aide d'une filtration voisine de la filtration de Hodge asymptotique.

/pdf/algorithme-de-calcul-du-polynome-de-bernstein-cas-non-1o0nwnk0zu.pdf

Algorithme de calcul du polynôme de Bernstein : Cas non dégénéré

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Algorithme de calcul du polynôme de Bernstein : Cas non dégénéré