The purpose of this study was to characterize the prevalence of taper damage in modular TKA components. One hundred ninety-eight modular components were revised after 3.9±4.2 years of implantation. Modular components were evaluated for fretting corrosion using a semi-quantitative 4-point scoring system. Design features and patient information were assessed as predictors of fretting corrosion da...

After formulating Conjecture A for p-adic L-functions defined over ordinary Hilbert modular Hida deformations on a totally real field F of degree d, we construct two p-adic L-functions of d+1-variable depending on the parity of weight as a partial result on Conjecture A. We will also state Conjecture B which is a corollary of Conjecture A but is important by itself. Main issues of the construct...

We are interested in understanding and describing the p-adic properties of Jacobi forms. As opposed to the case of modular forms, not much work has been done in this area. The literature includes [3, 4, 7]. In the first section, we follow Serre’s ideas from his theory of p-adic modular forms. We study Jacobi forms whose Fourier expansions have integral coefficients and look at congruences betwe...

A well known result is that if E2k is the Eisenstein series of weight 2k and 2k = 2k′ (mod (p− 1)p), then E2k = E2k′ (mod p). In words, this result tells us that the Eisenstein series form a natural family of modular forms that are p-adically interpolated in the weight aspect. Motivated by a question of Serre, we construct a second natural family of modular forms that have this same property. B...

These lectures concern the arithmetic of modular curves, and in particular the geometry of integral models of modular curves in the neighborhood of their singular points. These singularities only appear modulo p. If X is a modular curve and x is a singular point, then the nature of the singularity is measured by the completed local ring ÔX,x. Let us first review the basics of integral models of...

Abstract. Generalizing work of Zagier, in an important recent paper Bruinier and Funke prove that the generating functions for traces of singular values of many modular functions are weight 3 2 modular forms. Using facts about half-integral weight modular forms, we obtain identities relating traces of singular moduli for modular functions of level p and 1. These follow from a general result rel...

We join Hurwitz space constructions and the universal Frattini cover of a nite group The goal is to form and apply generalizations of the towers X p X p X p of modular curves This generalization relies on the appearance of the dihedral group Dp and its companion group Zp f g in the theory of modular curves We replace Dp by any nite group G and p by any prime dividing the order of G The replacem...

In his letter (Serre, 1996), J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions A×B/B × → Fp, where B is the endomorphism algebra of a supersingular elliptic curve. We generalize this result to Siegel modular forms, proving that the systems of Hecke eigenvalues given by Siegel modular forms (mod p)...

We show that if F is a totally real field in which p splits completely and f is a mod p Hilbert modular form with parallel weight 2 < k < p, which is ordinary at all primes dividing p and has tamely ramified Galois representation at all primes dividing p, then there is a “companion form” of parallel weight k′ := p + 1 − k. This work generalises results of Gross and Coleman–Voloch for modular fo...

(an 2 1 Fp) of such a form, μ is given by qd=dq: It lifts, by the same formula, to the space of p-adic modular forms. This suggests a relation with the Tate twist of the mod p Galois representation attached to f; if the latter is a Hecke eigenform. Over C; this operator has been considered already by Ramanujan, where it fails to preserve modularity “by a multiple of E2": Maass modi...ed it so t...