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1.1. The problem. Let f be a cuspidal newform for Γ1(N) with weight k ≥ 2 and character ε. There are well-established methods for computing such forms using modular symbols, see [Ste07]. Let πf be the corresponding automorphic representation of the adèle group GL2(AQ). (As there are numerous possible normalisations, we shall recall the construction in(More)
I present a general theory of overconvergent p-adic automorphic forms and eigenvarieties for connected reductive algebraic groups G whose real points are compact modulo centre, extending earlier constructions for forms of GLn due to Buzzard, Chenevier and Yamagami. This leads to some new phenomena, including the appearance of intermediate spaces of "(More)
This paper studies Emerton's Jacquet module functor for locally analytic representations of p-adic reductive groups, introduced in [Eme06a]. When P is a parabolic subgroup whose Levi factor M is not commutative, we show that passing to an isotypical subspace for the derived subgroup of M gives rise to essentially admissible locally analytic representations(More)
Renal cell carcinoma is a common cancer, known for its aggressive behavior and ability to metastasize nearly every organ system in the body. While the cancer commonly spreads to a select few organs and metastasis usually develops within 5 years of diagnosis, there have been numerous case reports of atypical sites of metastasis and cases of relapse up to(More)
Proposition 4.1 (1) of this article is not correct as stated. For instance, if ε is the quadratic Dirichlet character of conductor 15, then there are two newforms in S k (Γ 1 (15), ε) with coefficients in Q, and these are twists of each other by the quadratic character of conductor 3, whereas the quantity u in the proposition is 0 here. I am grateful to(More)