In [6] the second author proved that the image of the Galois representation mod λ attached to a Hilbert modular newform is “large” for all but finitely many primes λ, if the form is not a theta series. In this brief note, we give an explicit bound for this exceptional finite set of primes and determine the images in three different examples. Our examples are of Hilbert newforms on real quadrati...

Let (R,m) be a Noetherian local ring, M be a finitely generated R-module of dimension n and a be an ideal of R. In this paper, generalizing the main results of Dibaei and Jafari [3] and Rezaei [8], we will show that if T is a subset of AsshR M, then there exists an ideal a of R such that AttR Hna (M)=T. As an application, we give some relationships between top local cohomology modules and top f...

In this article, we distinguish Siegel cuspidal eigenforms of degree two on the full symplectic group from signs their Hecke eigenvalues. To establish our theorem, obtain a result towards simultaneous sign changes eigenvalues eigenforms. course proof, also prove that Satake p-parameters different are distinct for set primes p density 1. The main ingredient to latter is theory Galois representat...

We give an effective version of a result reported by Serre asserting that the images of the Galois representations attached to an abelian surface with End(A) = Z are as large as possible for almost every prime. Our algorithm depends on the truth of Serre’s conjecture for two dimensional odd irreducible Galois representations. Assuming this conjecture we determine the finite set of primes with e...

If E is an elliptic curve over Q, then let E(D) denote the D−quadratic twist of E. It is conjectured that there are infinitely many primes p for which E(p) has rank 0, and that there are infinitely many primes ` for which E(`) has positive rank. For some special curves E we show that there is a set S of primes p with density 1 3 for which if D = Q pj is a squarefree integer where pj ∈ S, then E...

In this paper we propose an algorithm for computing large primes p and q such that q divides p4 + p3 + p2 + p+ 1 or p4 − p3 + p2 − p+ 1. Such primes are key parameters for the GiulianiGong Public Key System.