9,224 research outputs found
Shtukas and the Taylor expansion of -functions (II)
For arithmetic applications, we extend and refine our results in \cite{YZ} to
allow ramifications in a minimal way. Starting with a possibly ramified
quadratic extension of function fields over a finite field in odd
characteristic, and a finite set of places of that are unramified
in , we define a collection of Heegner--Drinfeld cycles on the moduli stack
of -Shtukas with -modifications and Iwahori level
structures at places of . For a cuspidal automorphic representation
of with square-free level ,
and whose parity matches the root number of ,
we prove a series of identities between: (1) The product of the central
derivatives of the normalized -functions , where is the quadratic
id\`ele class character attached to , and ; (2) The self
intersection number of a linear combination of Heegner--Drinfeld cycles. In
particular, we can now obtain global -functions with odd vanishing orders.
These identities are function-field analogues of the formulas of Waldspurger
and Gross--Zagier for higher derivatives of -functions.Comment: 90 page
Bell Inequality in the Holographic EPR Pair
We study the Bell inequality in a holographic model of the casually
disconnected Einstein-Podolsky-Rosen (EPR) pair. The
Clauser-Horne-Shimony-Holt(CHSH) form of Bell inequality is constructed using
holographic Schwinger-Keldysh (SK) correlators. We show that the manifestation
of quantum correlation in Bell inequality can be holographically reproduced
from the classical fluctuations of dual accelerating string in the bulk
gravity. The violation of this holographic Bell inequality supports the
essential quantum property of this holographic model of an EPR pair.Comment: 8 pages, 2 figures; references and texts added; v3: matches published
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