Abstract:
We consider L-functions L1,..., Lk from the Selberg class which have polynomial Euler product and satisfy Selberg's orthonormality condition. We show that on every vertical line s = σ + it with σ ∈ (1/2, 1), these L-functions simultaneously take large values of size exp(c (log t)1−σ/log log t inside a small neighborhood. Our method extends to σ = 1 unconditionally, and to σ = 1/2 on the generalized Riemann hypothesis. We also obtain similar joint omega results for arguments of the given L-functions.