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editI'm confused about the need for an ε in condition ii). Should this not be " for some fixed positive real number r and any ε>0"?
Is (iii) right? It looks backwards to me.
I'm used to seeing phi(z) = gamma factor times original Dirichlet series, then the functional equation is phi(z) = <some number of absolute value 1> times the complex conjugate of phi(1 - complex conjugate of z) Virginia-American (talk) 02:48, 25 February 2008 (UTC)
The second reference (Conrey & Ghosh) state it the way I would expect. I will edit the article Virginia-American (talk) 03:21, 25 February 2008 (UTC)
The sentence "The condition that is important, as the case includes the Dirichlet eta-function, which violates the Riemann hypothesis." is not true: the Dirichlet eta does not violate RH, it just doesn't have a pole at . The function violates RH as noted in paper [2]. — Preceding unsigned comment added by 95.168.124.177 (talk) 12:25, 9 November 2018 (UTC)
Examples
editThe statement about Fχ can't be right if χ is nontrivial. Take for example , which is in the Selberg class. Then is the Dirichlet L-function of an imprimitive principal character, and therefore not in the Selberg class.—Emil J. 23:41, 11 June 2014 (UTC)