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Topics on Modular Galois Representations Modulo Prime Powers

In: Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory

Author

Listed:
  • Panagiotis Tsaknias

    (Unité de Recherche en Mathématiques, Université du Luxembourg)

  • Gabor Wiese

    (Unité de Recherche en Mathématiques, Université du Luxembourg)

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.

Suggested Citation

  • Panagiotis Tsaknias & Gabor Wiese, 2017. "Topics on Modular Galois Representations Modulo Prime Powers," Springer Books, in: Gebhard Böckle & Wolfram Decker & Gunter Malle (ed.), Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, pages 741-763, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-70566-8_31
    DOI: 10.1007/978-3-319-70566-8_31
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