My question is about connectedness of the Riemann zeta function and the theory of Bergman spaces. Because I'm working in this area of Bergman spaces, and I had Analytic number theory as a subject on my graduate studies, I would like to know more about applications of the theory of Bergman spaces to Analytic number theory. By Bergman space I mean a space of all holomorphic functions on some domain that are $L^{p}$ there, i.e. the theory of Bergman spaces from the book of Kehe Zhu. Is there any equivalent of Riemann hypothesis in the theory of Bergman spaces? I would like to know more about the intersection between the Analytic number theory and the theory of Bergman spaces(Kehe Zhu). 



Riemann zeta function in the framework of Bergman spaces
I am not aware of such an "Riemann" conjecture in the theory of Bergman spaces. However,
a result which lies perhaps "in the intersection" of both areas is *Voronin's Universality Theorem*, about the universality of zeta-functions, i.e., the property of zeta-functions (and Dirichlet $L$-functions) to approximate arbitrary non-vanishing holomorphic functions arbitrarily well. The proof uses theory of Bergman spaces, see S.M. Voronin, "Theorem on the Universality of the Riemann Zeta Function." Izv. Akad. Nauk SSSR, Ser. Matem. 39, (1975) pp.475-486.


