So far there is no systematic attempt to construct Boolean functions with maximum annihilator immunity. In this paper we present a construction keeping in mind the basic theory of annihilator immunity. This construction provides functions with the maximum possible annihilator immunity and the weight, nonlinearity and algebraic degree of the functions can be properly calculated under certain cas...

Motivated by arithmetic applications, we introduce the notion of a partial zeta function which generalizes the classical zeta function of an algebraic variety defined over a finite field. We then explain two approaches to the general structural properties of the partial zeta function in the direction of the Weil type conjectures. The first approach, using an inductive fibred variety point of vi...

We prove that the theta correspondence for the dual pair (S̃L2, PB×), for B an indefinite quaternion algebra over Q, preserves rationality and p-integrality in both directions. As a consequence, we deduce the rationality of certain period ratios of modular forms and even p-integrality of these ratios under the assumption that p does not divide a certain L-value. The rationality is applied to giv...

The purpose of this paper is to prove that certain subquotients of the MF∇-objects of Faltings ([1]) are semi-positive. In particular, we obtain an algebraic proof of a result (generalizing those of [5], [9]) on the semi-positivity of the higher direct images of certain kinds of sheaves for semistable families of algebraic varieties. Our Main Theorem, proven in §3, is as follows: Theorem 3.4: L...

Spectra attacks proposed recently are more data efficient than algebraic attacks against stream cipher. They are also time-andspace efficient. A measurement of the security of a stream cipher against spectra attacks is spectral immunity, the lowest spectral weight of the annihilator of the key stream. We study both the annihilator and the spectral immunity. We obtain a necessary and sufficient ...

Let K be a field of characteristic 0 and S = K[x1, . . . , xn] the polynomial ring over K with graded maximal ideal m = (x1, . . . , xn). Denote by βi(M) = Tor S i (K,M) the ith Betti number of a finitely generated graded module M and by Gin(I) the generic initial ideal of a graded ideal I with respect to the reverse lexicographical order. In this paper we answer (positively) a question raised ...

If F is a global function field of characteristic p > 3, we employ Tate’s theory of analytic uniformization to give an alternative proof of a theorem of Igusa describing the image of the natural Galois representation on torsion points of non-isotrivial elliptic curves defined over F . Along the way, using basic properties of Faltings heights of elliptic curves, we offer a detailed proof of the ...

A right Johns ring is a Noetherian in which every ideal annihilator. It known that RR the Jacobson radical J(R)J(R) of nilpotent and Soc(R)(R) an essential RR. Moreover, Kasch, is, simple RR-module can be embedded For M∈RM∈R-Mod we use concept MM-annihilator define module (resp. quasi-Johns) as MM such submodule MM-annihilator. called quasi-Johns if any set submodules satisfies ascending chain ...

We use a refined version of Roth’s Lemma, proved with the help of Faltings’ Product Theorem, in order to give an upper bound for the multiplicity of a binary linear recurrence. Résumé Nous utilisons une version du Lemme de Roth, provenant du Théorème du Produit de Faltings, pour majorer la multiplicité d’une récurrence linéaire binaire. Version française abrégée Dans l’article [7] H.-P. Schlick...