Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/96846
 Title: On modular forms and the inverse Galois problem Author: Dieulefait, L. V. (Luis Victor)Wiese, Gabor Keywords: Grups discontinusFormes automòrfiquesTeoria de nombresDiscontinuous groupsAutomorphic formsNumber theory Issue Date: Sep-2011 Publisher: American Mathematical Society (AMS) Abstract: In this article new cases of the inverse Galois problem are established. The main result is that for a fixed integer $n$, there is a positive density set of primes $p$ such that $\mathrm{PSL}_2(\mathbb{F}_{p^n})$ occurs as the Galois group of some finite extension of the rational numbers. These groups are obtained as projective images of residual modular Galois representations. Moreover, families of modular forms are constructed such that the images of all their residual Galois representations are as large as a priori possible. Both results essentially use Khare's and Wintenberger's notion of good-dihedral primes. Particular care is taken in order to exclude nontrivial inner twists. Note: Reproducció del document publicat a: http://dx.doi.org/10.1090/S0002-9947-2011-05477-2 It is part of: Transactions of the American Mathematical Society, 2011, vol. 363, num. 9, p. 4569-4584 Related resource: http://dx.doi.org/10.1090/S0002-9947-2011-05477-2 URI: http://hdl.handle.net/2445/96846 ISSN: 0002-9947 Appears in Collections: Articles publicats en revistes (Matemàtiques i Informàtica)

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