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A note on simple $a$-points of $L$-functions

A note on simple $a$-points of $L$-functions

We prove, subject to certain hypotheses, that a positive proportion of the $a$-points of the Riemann zeta-function and Dirichlet $L$-functions with primitive characters are simple and discuss corresponding results for other functions in the Selberg class. We also prove an unconditional result of this type for the $a$-points in fixed …