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Let E/Q be a real quadratic field and π0 a cuspidal, irreducible, automorphic representation of GL(2,AE) with trivial central character and infinity type (2,2n+2) for some non-negative integer n. We show that there exists a non-zero Siegel paramodular newform F:H2→C with weight, level, Hecke eigenvalues, epsilon factor and L-function determined explicitly by π0. We tabulate these invariants in terms...
We consider a variant of a question of N. Koblitz. For an elliptic curve E/Q which is not Q-isogenous to an elliptic curve with torsion, Koblitz has conjectured that there exists infinitely many primes p such that Np(E)=#E(Fp)=p+1−ap(E) is also a prime. We consider a variant of this question. For a newform f, without CM, of weight k⩾4, on Γ0(M) with trivial Nebentypus χ0 and with integer Fourier coefficients,...
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