Download Frontiers in Number Theory, Physics, and Geometry II: On by Don Zagier (auth.), Pierre Cartier, Pierre Moussa, Bernard PDF
By Don Zagier (auth.), Pierre Cartier, Pierre Moussa, Bernard Julia, Pierre Vanhove (eds.)
The relation among arithmetic and physics has a protracted historical past, within which the function of quantity conception and of alternative extra summary elements of arithmetic has lately turn into extra prominent.
More than ten years after a primary assembly in 1989 among quantity theorists and physicists on the Centre de body des Houches, a moment 2-week occasion all in favour of the wider interface of quantity conception, geometry, and physics.
This ebook is the results of that interesting assembly, and collects, in 2 volumes, prolonged models of the lecture classes, through shorter texts on specified themes, of eminent mathematicians and physicists.
The current quantity has 3 components: Conformal box Theories, Discrete teams, Renomalization.
The better half quantity is subtitled: On Random Matrices, Zeta features and Dynamical structures (Springer, 3-540-23189-7).
Read Online or Download Frontiers in Number Theory, Physics, and Geometry II: On Conformal Field Theories, Discrete Groups and Renormalization PDF
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Extra info for Frontiers in Number Theory, Physics, and Geometry II: On Conformal Field Theories, Discrete Groups and Renormalization
Example text
Thus one of the many virtues of the mysterious dilogarithm is that it gives, at least conjecturally, an effective way of calculating the orders of certain groups in algebraic K-theory! To conclude, we mention that Borel’s work connects not only K3ind (F ) and ind (F ) and ζF (m) for any integer m > 1. No ζF (2) but more generally K2m−1 elementary description of the higher K-groups analogous to the description of K3 in terms of B is known, but one can at least speculate that these groups and their regulator mappings may be related to the higher polylogarithms and that, more specifically, the value of ζF (m) is always a simple multiple of a determinant (r2 × r2 or (r1 + r2 ) × (r1 + r2 ) depending whether m is even or odd) whose entries are linear combinations of values of the BlochWigner-Ramakrishnan function Dm (z) with arguments z ∈ F .
13 . . and values of Dedekind zeta functions . . . . . . . . . . . . . 16 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Notes on Chapter I . . . . . . . . . . . . . . . . . . . . . . 21 II. 1. 2. 3. 4. Further aspects of the dilogarithm . . . . . . . . . . . . 22 Variants of the dilogarithm function . . . . . . . . . . . . . . . Dilogarithm identities . . . . .
21 II. 1. 2. 3. 4. Further aspects of the dilogarithm . . . . . . . . . . . . 22 Variants of the dilogarithm function . . . . . . . . . . . . . . . Dilogarithm identities . . . . . . . . . . . . . . . . . . . . . Dilogarithms and modular functions: the Nahm equation . . . . . . Higher polylogarithms . . . . . . . . . . . . . . . . . . . . . 22 33 41 58 References . . . . . . . . . . . . .