Topics on Modular Galois Representations Modulo Prime Powers

Panagiotis Tsaknias () and Gabor Wiese ()
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Panagiotis Tsaknias: Unité de Recherche en Mathématiques, Université du Luxembourg
Gabor Wiese: Unité de Recherche en Mathématiques, Université du Luxembourg

A chapter in Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, 2017, pp 741-763 from Springer

Abstract: Abstract This article surveys modularity, level raising and level lowering questions for two-dimensional representations modulo prime powers of the absolute Galois group of the rational numbers. It contributes some new results and describes algorithms and a database of modular forms orbits and higher congruences.

Keywords: Modular forms; Galois representations; Modularity higher congruences; Level raising; Level lowering; Database; 11F33; 11F80 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-70566-8_31

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DOI: 10.1007/978-3-319-70566-8_31

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