I juste googled to get some insight about universality for l-functions belonging to the Selberg class, but it seems that the proof requires the validity of the prime number theorem for the considered l-functions. Still, Yoshikatsu Yashiro uploaded a preprint on Arxiv pretending to give an unconditional proof of this prime number theorem for the whole Selberg class. So, has universality for all l-functions in the Selberg class been definitely established?
Thanks in advance.
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asked Apr 30, 2014 at 17:17
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$\begingroup$ Please add references. $\endgroup$– Marc PalmCommented Apr 30, 2014 at 17:33
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$\begingroup$ The first article can be found there:link.springer.com/article/10.1007%2Fs10986-010-9087-z $\endgroup$– Sylvain JULIENCommented Apr 30, 2014 at 17:42
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$\begingroup$ And the second one there:arxiv.org/abs/1311.0754 $\endgroup$– Sylvain JULIENCommented Apr 30, 2014 at 17:45
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$\begingroup$ Did you ask the author via email? $\endgroup$– Marc PalmCommented Apr 30, 2014 at 17:51
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$\begingroup$ No. By the way, which author do you talk about? Yoshikatsu Yashiro? $\endgroup$– Sylvain JULIENCommented Apr 30, 2014 at 17:53
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