The question is in the title: has a universality theorem in the sense of Voronin been proved for the DavenportHeilbronn function, or do we expect such a theorem to hold true only for L functions that are supposed to verify the analogue of the Riemann Hypothesis?
Thanks in advance.



http://siauliaims.su.lt/pdfai/2008/laurincikas08.pdf
For irrational $q$, the requirements are true (see Corollary 2). Interesting side remark:


