Trivial L-functions for the rational function field
نویسنده
چکیده
In this paper, we will study an extreme case of cancellation over the rational function field k = E(T ). If we assume that the geometric Galois group Gal(k/kE) has no non-trivial invariants on V and that the degree f(V ) of the Artin conductor of V is twice the dimension of V , then L(V, s) is a polynomial of degree 0 in q with constant coefficient 1. Hence L(V, s) = 1 is a constant function! We call these trivial L-functions for the rational function field (although we will see that they arise in many non-trivial situations).
منابع مشابه
HYPERTRANSCENDENTAL FORMAL POWER SERIES OVER FIELDS OF POSITIVE CHARACTERISTIC
Let $K$ be a field of characteristic$p>0$, $K[[x]]$, the ring of formal power series over $ K$,$K((x))$, the quotient field of $ K[[x]]$, and $ K(x)$ the fieldof rational functions over $K$. We shall give somecharacterizations of an algebraic function $fin K((x))$ over $K$.Let $L$ be a field of characteristic zero. The power series $finL[[x]]$ is called differentially algebraic, if it satisfies...
متن کاملA method to obtain the best uniform polynomial approximation for the family of rational function
In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion, we obtain the best uniform polynomial approximation out of P2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. Using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...
متن کاملTOPOLOGY OPTIMIZATION OF PLANE STRUCTURES USING BINARY LEVEL SET METHOD AND ISOGEOMETRIC ANALYSIS
This paper presents the topology optimization of plane structures using a binary level set (BLS) approach and isogeometric analysis (IGA). In the standard level set method, the domain boundary is descripted as an isocountour of a scalar function of a higher dimensionality. The evolution of this boundary is governed by Hamilton–Jacobi equation. In the BLS method, the interfaces of subdomai...
متن کاملOn characterizations of the fully rational fuzzy choice functions
In the present paper, we introduce the fuzzy Nehring axiom, fuzzy Sen axiom and weaker form of the weak fuzzycongruence axiom. We establish interrelations between these axioms and their relation with fuzzy Chernoff axiom. Weexpress full rationality of a fuzzy choice function using these axioms along with the fuzzy Chernoff axiom.
متن کاملSignal detection Using Rational Function Curve Fitting
In this manuscript, we proposed a new scheme in communication signal detection which is respect to the curve shape of received signal and based on the extraction of curve fitting (CF) features. This feature extraction technique is proposed for signal data classification in receiver. The proposed scheme is based on curve fitting and approximation of rational fraction coefficients. For each symbo...
متن کامل