We introduce the notion of quasi-inner function and show that product u = ρ ∞ ∏ v m + 1 ratios local L -factors ( z ) γ / − over a finite set F places Q inclusive archimedean place is on left critical line ℜ 2 in following sense. The off diagonal part 21 matrix multiplication by orthogonal decomposition Hilbert space square integrable functions into Hardy H its complement compact operator. When...

In this article, we show that the Goldman–Iwahori metric on space of all norms a fixed vector satisfies Helly property for balls. On non-Archimedean side, deduce most classical Bruhat–Tits buildings may be endowed with natural piecewise ? ? $\ell ^\infty$ which is injective. We also prove semisimple groups over local fields act properly and cocompactly graphs. This gives another proof biautomat...