Galois representations and Hecke operators associated with the mod- $p$ cohomology of $GL(m(p-1),\mathbb{Z})$

1998 ◽  
Vol 227 (4) ◽  
pp. 685-703 ◽  
Author(s):  
Avner Ash ◽  
Rajesh Manjrekar
Keyword(s):  
Galois Representations ◽  
Hecke Operators ◽  
Mod P

scholarly journals Hecke operators on differential modular forms mod p

2012 ◽  
Vol 132 (5) ◽  
pp. 966-997 ◽  
Author(s):  
Alexandru Buium ◽  
Arnab Saha
Keyword(s):  
Modular Forms ◽  
Hecke Operators ◽  
Differential Modular Forms ◽  
Mod P

scholarly journals Twisting of Siegel paramodular forms

2017 ◽  
Vol 13 (07) ◽  
pp. 1755-1854 ◽  
Author(s):  
Jennifer Johnson-Leung ◽  
Brooks Roberts
Keyword(s):  
Number Theory ◽  
Explicit Expression ◽  
Dirichlet Character ◽  
Hecke Operators ◽  
Commutation Relations ◽  
Mod P

Let Sk(Γpara(N)) be the space of Siegel paramodular forms of level N and weight k. Fix an odd prime p ∤ N and let χ be a nontrivial quadratic Dirichlet character mod p. Based on [Twisting of paramodular vectors, Int. J. Number Theory 10 (2014) 1043–1065], we define a linear twisting map 𝒯χ : Sk(Γpara(N)) → Sk(Γpara(Np4)). We calculate an explicit expression for this twist, give the commutation relations of this map with the Hecke operators and Atkin–Lehner involution for primes ℓ ≠p, and prove that the L-function of the twist has the expected form.

scholarly journals Computing the number of certain Galois representations mod p

2011 ◽  
Vol 23 (3) ◽  
pp. 603-627 ◽  
Author(s):  
Tommaso Giorgio Centeleghe
Keyword(s):  
Galois Representations ◽  
Mod P
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