Let p be a prime $$\ge 5$$ . We establish explicit rates of overconvergence for some members the “Eisenstein family”, notably p-adic modular function $$V(E_{(1,0)}^{*})/E_{(1,0)}^{*}$$ (V Frobenius operator) that plays pivotal role in Coleman’s theory families forms. The proof goes via an in-depth analysis functions form $$V(E_k)/E_k$$ where $$E_k$$ is classical Eisenstein series level 1 and we...

Polynomial-time algorithms are given to find a central decomposition of maximum size for a finite p-group of class 2 and for a nilpotent Lie ring of class 2. The algorithms use Las Vegas probabilistic routines to compute the structure of finite ∗-rings and also the Las Vegas C-MeatAxe. When p is small, the probabilistic methods can be replaced by deterministic polynomial-time algorithms. The me...

purpose : the aim of this study is to measure the endogenous cortisol levels in the patients with central serous chorioretinopathy (cscr) and also, evaluate the short-term effect of oral ketoconazole in the treatment of both acute and chronic cscr. methods : in this prospective interventional case series 12 patients with acute cscr and 7 patients with chronic cscr (including one patient with bi...