منابع مشابه
Evaluating Igusa functions
The moduli space of principally polarized abelian surfaces is parametrized by three Igusa functions. In this article we investigate a new way to evaluate these functions by using Siegel Eisenstein series. We explain how to compute the Fourier coefficients of certain Siegel modular forms using classical modular forms of halfintegral weight. One of the results in this paper is an explicit algorit...
متن کاملMotivic Igusa Zeta Functions
Let p be a prime number and let K be a finite extension of Qp. Let R be the valuation ring of K, P the maximal ideal of R, and K̄ = R/P the residue field of K. Let q denote the cardinality of K̄, so K̄ ≃ Fq. For z in K, let ord z denote the valuation of z, and set |z| = q . Let f be a non constant element of K[x1, . . . , xm]. The p-adic Igusa local zeta function Z(s) associated to f (relative to ...
متن کاملOn Simple Igusa Local Zeta Functions
The objective of this announcement is the statement of some recent results on the classiication of generalized Igusa local zeta functions associated to irreducible matrix groups. The deenition of a simple Igusa local zeta function will motivate a complete classiication of certain generalized Igusa local zeta functions associated to simply connected simple Chevalley groups. In addition to the no...
متن کاملIgusa zeta functions and motivic generating series
Proefschrift ingediend tot het behalen van de graad van Doctor in de Wetenschappen december 2004 ii Introduction Let f be a polynomial in Z[x], x = (x 1 ,. .. , x m), defining a hypersurface X 0 in A m Z. Igusa's Monodromy Conjecture predicts an intriguing relationship between the arithmetic properties of f , and the topology of the (not necessarily reduced) complex hypersurface X 0 = X 0 × Spe...
متن کاملThe Igusa local zeta functions of elliptic curves
We determine the explicit form of the Igusa local zeta function associated to an elliptic curve. The denominator is known to be trivial. Here we determine the possible numerators and classify them according to the KodairaNéron classification of the special fibers of elliptic curves as determined by Tate’s algorithm.
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2014
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2014-02816-0