For every epsilon>0 and fixed pi', L(s,pi) and L(s,pi×pi') are claimed to be lower bounded and zero-free in a c C_pi^{-epsilon} neighborhood of Re(s)=1, with ineffective c.
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Power sums and Siegel-type zero-free regions for L-functions
For every epsilon>0 and fixed pi', L(s,pi) and L(s,pi×pi') are claimed to be lower bounded and zero-free in a c C_pi^{-epsilon} neighborhood of Re(s)=1, with ineffective c.