A theorem of Christol states that a power series over a finite field is algebraic over the polynomial ring if and only if its coefficients can be generated by a finite automaton. Using Christol’s result, we prove that the same assertion holds for generalized power series (whose index sets may be arbitrary well-ordered sets of nonnegative rationals).

Generation of 1 and k chain scFv fragments against thyroid peroxidase by combinatorial libraries: Evidence for both 1 and k chain-secreting lymphocytes in the thyroid from patients with Graves’ disease Nicolas Chapal, Thierry Chardès, Damien Bresson, Martine Pugnière, Jean-Claude Mani, Bernard Pau, Majida Bouanani and Sylvie Péraldi-Roux CNRS-UMR 5094, Faculté de Pharmacie, Montpellier, France ...

reasonable adult dose and, for this child, 1 mg kg. There are no available data concerning the likely absorption of corticosteroid from a topical preparation such as Eumovate in a child of this age; however, it would be a coincidence if this event were not involved in the development of GPP in this case. While unlikely to be a common occurrence in everyday clinical practice it does appear that ...

We consider variational properties of some numerical invariants, measuring convergence of local horizontal sections, associated to differential modules on polyannuli over a nonarchimedean field of characteristic zero. This extends prior work in the onedimensional case of Christol, Dwork, Robba, Young, et al. Our results do not require positive residue characteristic; thus besides their relevanc...

Building on work of Crew, we give a rigid cohomological analogue of the main result of Deligne’s “Weil II”; this makes it possible to give a purely p-adic proof of the Weil conjectures. Ingredients include a p-adic analogue of Laumon’s application of the geometric Fourier transform in the l-adic setting, as well as recent results on p-adic differential equations, due to André, Christol, Crew, M...

Let K be an algebraically closed field of characteristic p. We exhibit a counterexample against a theorem asserted in one of our earlier papers, which claims to characterize the integral closure of K((t)) within the field of Hahn-Mal’cev-Neumann generalized power series. We then give a corrected characterization, generalizing our earlier description in terms of finite automata in the case where...

For more on the Tate curve (which we will not use directly) and for standard facts on modular forms (which we will use later), see [S, Chap. 5; M. Chap. 1], respectively. Voloch's nice proof involved approximating q by algebraic quantities and getting a contradiction by analyzing the Galois action using Igusa's theorem. We offer below a proof based on the criterion of algebraicity due to Christ...