We investigate certain finiteness questions that arise naturally when studying approximations modulo prime powers of p-adic Galois representations coming from modular forms. We link these finiteness statements with a question by K. Buzzard concerning p-adic coefficient fields of Hecke eigenforms. Specifically, we conjecture that for fixed N , m, and prime p with p not dividing N , there is only...

Let F be a totally real field, p ≥ 3 a rational prime unramified in F , and p a place of F over p. Let ρ : Gal(F/F ) → GL2(Fp) be a two-dimensional mod p Galois representation which is assumed to be modular of some weight and whose restriction to a decomposition subgroup at p is irreducible. We specify a set of weights, determined by the restriction of ρ to inertia at p, which contains all the ...

The Forest Buzzard Buteo oreophilus rizonatus, confined to the temperate coastal and escarpment forests of South Africa (Hockey et al. 2005), is often considered to be a subspecies of the Mountain Buzzard Buteo oreophilus of the forested highlands of East Africa, following Siegfried (1971) and Siegfried and Frost (1973). However, both taxa are largely resident, with breeding distributions separ...

Crystabelline representations are of the absolute Galois group $$\smash {G_{\mathbb {Q}_p}}$$ over {\smash {\overline{\mathbb {Q}}_p}}$$ that become crystalline on {G_{F}}$$ for some abelian extension {F/\mathbb {Q}_p}$$ . Their relation to modular forms is representation associated with a finite slope newform level divisible by {p^2}$$ crystabelline. In this article, we study connection betwee...

-we studied the breeding performance of a Grey Eagle-Buzzard (Geranoaetus melanoleucus) population in a region of northern Argentinian Patagonia where two different habitats occur; the mountains near the Andean cordillera and the plains where shrub-steppes predominate. Mean eagle density was 1 pair/l9 km2 (N = 44), with higher densities occuring in the plains (1 pair03.2 km2, N = 17) than in th...

We present a finite difference method for modeling the propagation of electrical waves in cardiac tissue using the cable equation with homogeneous Neumann boundary conditions. This method is novel in that it is derived by first discretizing the phase field method as described by Fenton, et al, then taking a limit to recover a sharp interface. Our method provides for exact voltage conservation (...

In submammalian vertebrates the optic tectum, a structure homologous with the mammalian superior colliculus, is the primary way-station of the fibers of the optic tract. As such, it is assumed to be of central significance in the coordination of visually-guided behavior (Huber and Crosby, '33; Ariens Kappers, Huber and Crosby, '36) . Ascending the evolutionary scale, the superior colliculus of ...