Non-Euclidean Structure of the family of zeta-functions

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The aim of my project was to extend, to certain family of zeta-functions, the findings that had been obtained by myself in an extensive study of the Riemann zeta-function. In particular, the main object of the research was to analyze a hyperbolic (i.e., non-Euclidean) structure that seemed to govern the whole family, which should open a new perspective over the entire theory of zeta-functions.To these effects, we obtained :(1) A new proof of Kuznetsou's trace-formula over the hyperbolic upper-half-space.(2) A proof of the trace formula over the hyperbolic upper-half-space.(3) A new relation between Dedekind zeta-functions of quadratic number fields and Hecke congruence groups.Those results were reported as invited lectures at(i) The 39th Taniguchi International Symposium (organized by Y.Motohashi) : 1996(ii) International Symposium on Analytic Number Theory (organized by Hong Kong Univ.) : 1997(iii) International Symposium on Analytic Number Theory (organized by Polish Academy) : 1997Further, it should be noted that the whole research result was published by Cambridge University Press in a volume of their Mathematical Tracts Series.