scholarly journals Compatible systems of symplectic Galois representations and the inverse Galois problem I. Images of projective representations

2016 ◽  
Vol 369 (2) ◽  
pp. 887-908 ◽  
Author(s):  
Sara Arias-de-Reyna ◽  
Luis Dieulefait ◽  
Gabor Wiese
Keyword(s):  
Galois Representations ◽  
Inverse Galois Problem ◽  
Projective Representations

Polynomials for projective representations of level one forms

2011 ◽  
Author(s):  
Johan Bosman
Keyword(s):  
Modular Forms ◽  
Galois Representations ◽  
Cusp Forms ◽  
Tau Function ◽  
Projective Representations ◽  
Level 1

This chapter explicitly computes mod-ℓ Galois representations attached to modular forms. To be precise, it looks at cases with l ≤ 23, and the modular forms considered will be cusp forms of level 1 and weight up to 22. The chapter presents the result in terms of polynomials associated with the projectivized representations. As an application, it will improve a known result on Lehmer's nonvanishing conjecture for Ramanujan's tau function.

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