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Riemann zeta function
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===Universality=== The critical strip of the Riemann zeta function has the remarkable property of '''universality'''. This [[zeta function universality]] states that there exists some location on the critical strip that approximates any [[holomorphic function]] arbitrarily well. Since holomorphic functions are very general, this property is quite remarkable. The first proof of universality was provided by Sergei Mikhailovitch Voronin in 1975.<ref>{{cite journal|last=Voronin|first=S. M.|date=1975|title=Theorem on the Universality of the Riemann Zeta Function|journal=Izv. Akad. Nauk SSSR, Ser. Matem.|volume=39|pages=475–486}} Reprinted in ''Math. USSR Izv.'' (1975) '''9''': 443–445.</ref> More recent work has included [[Zeta function universality#Effective universality|effective]] versions of Voronin's theorem<ref>{{ cite journal |author1=Ramūnas Garunkštis |author2=Antanas Laurinčikas |author3=Kohji Matsumoto |author4=Jörn Steuding |author5=Rasa Steuding |title=Effective uniform approximation by the Riemann zeta-function |journal=Publicacions Matemàtiques |date=2010 |volume=54 |issue=1 |pages=209–219 |doi=10.5565/PUBLMAT_54110_12 |jstor=43736941 |url=http://ddd.uab.cat/record/52304 }}</ref> and [[Zeta function universality#Universality of other zeta functions|extending]] it to [[Dirichlet L-function]]s.<ref>{{ cite journal |author=Bhaskar Bagchi |title=A Joint Universality Theorem for Dirichlet L-Functions |journal=Mathematische Zeitschrift |issn=0025-5874 |volume=181 |issue=3 |date=1982 |pages=319–334 |doi=10.1007/bf01161980|s2cid=120930513 }}</ref><ref>{{cite book |last=Steuding |first=Jörn |date=2007 |title=Value-Distribution of L-Functions |volume=1877 |location=Berlin |publisher=Springer |page=19 |isbn=978-3-540-26526-9 |series=Lecture Notes in Mathematics |doi=10.1007/978-3-540-44822-8|arxiv=1711.06671 }}</ref>
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