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    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Commensurabilities Among Lattices in Pu (1, N). (Am-132), Volume 132

Commensurabilities Among Lattices in Pu (1, N). (Am-132), Volume 132

Deligne, Pierre R.
Mostow, George Daniel

Paperback

Series: Annals of Mathematics Studies, Book 132

CalculusGeometry

ISBN10: 0691000964
ISBN13: 9780691000961
Publisher: Princeton University Press
Published: Sep 12 1993
Pages: 218
Weight: 0.60
Height: 0.52 Width: 6.08 Depth: 9.22
Language: English

The first part of this monograph is devoted to a characterization of hypergeometric-like functions, that is, twists of hypergeometric functions in n-variables. These are treated as an (n+1) dimensional vector space of multivalued locally holomorphic functions defined on the space of n+3 tuples of distinct points on the projective line P modulo, the diagonal section of Auto P=m. For n=1, the characterization may be regarded as a generalization of Riemann's classical theorem characterizing hypergeometric functions by their exponents at three singular points.

This characterization permits the authors to compare monodromy groups corresponding to different parameters and to prove commensurability modulo inner automorphisms of PU(1, n).

The book includes an investigation of elliptic and parabolic monodromy groups, as well as hyperbolic monodromy groups. The former play a role in the proof that a surprising number of lattices in PU(1,2) constructed as the fundamental groups of compact complex surfaces with constant holomorphic curvature are in fact conjugate to projective monodromy groups of hypergeometric functions. The characterization of hypergeometric-like functions by their exponents at the divisors at infinity permits one to prove generalizations in n-variables of the Kummer identities for n-1 involving quadratic and cubic changes of the variable.

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