Proves an adelic open image theorem for Galois representations of genus two Siegel modular forms and obtains upper bounds on the size of sets where a_p equals a fixed complex number a.
MR 3135650 ↑2 [AS06] Mahdi Asgari and Freydoon Shahidi, Generic transfer from GSp(4) to GL(4), Compos
2 Pith papers cite this work. Polarity classification is still indexing.
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Under GRH, the count of primes p ≤ x with Frobenius trace a_{1,p}(A) = t is ≪ x to a power strictly less than 1, yielding that |a_{1,p}(A)| exceeds p to a positive power for almost all p.
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On the Lang--Trotter conjecture for Siegel modular forms
Proves an adelic open image theorem for Galois representations of genus two Siegel modular forms and obtains upper bounds on the size of sets where a_p equals a fixed complex number a.
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Bounds for the distribution of the Frobenius traces associated to a generic abelian variety
Under GRH, the count of primes p ≤ x with Frobenius trace a_{1,p}(A) = t is ≪ x to a power strictly less than 1, yielding that |a_{1,p}(A)| exceeds p to a positive power for almost all p.