1,098 research outputs found
Adelic Integrable Systems
Incorporating the zonal spherical function (zsf) problems on real and
-adic hyperbolic planes into a Zakharov-Shabat integrable system setting, we
find a wide class of integrable evolutions which respect the number-theoretic
properties of the zsf problem. This means that at {\it all} times these real
and -adic systems can be unified into an adelic system with an -matrix
which involves (Dirichlet, Langlands, Shimura...) L-functions.Comment: 23 pages, uses plain TE
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