## Contents of Volume 21, Number 1

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- On a theory of computation and complexity over the real numbers: $NP$- completeness, recursive functions and universal machines
- Lenore Blum, Mike Shub and Steve Smale PDF
- Bull. Amer. Math. Soc.
**21**(1989), 1-46

- Miscellaneous back pages, Bull. Amer. Math. Soc. (N.S.), Volume 21, Number 1 (1989)
- Bull. Amer. Math. Soc.
**21**(1989)

- Miscellaneous front pages, Bull. Amer. Math. Soc. (N.S.), Volume 21, Number 1 (1989)
- Bull. Amer. Math. Soc.
**21**(1989)

- Contributions to the $K$-theory of $C^*$-algebras of Toeplitz and singular integral operators
- Paul S. Muhly, Ian F. Putnam and Jingbo Xia PDF
- Bull. Amer. Math. Soc.
**21**(1989), 47-50

- Conjecture “Epsilon” for weight $k>2$
- Bruce W. Jordan and Ron Livné PDF
- Bull. Amer. Math. Soc.
**21**(1989), 51-56

- Iteration theory and inequalities for Kleinian groups
- F. W. Gehring and G. J. Martin PDF
- Bull. Amer. Math. Soc.
**21**(1989), 57-63

- Galois representations for Hilbert modular forms
- D. Blasius and J. Rogawski PDF
- Bull. Amer. Math. Soc.
**21**(1989), 65-69

- Every three-sphere of positive Ricci curvature contains a minimal embedded torus
- Brian White PDF
- Bull. Amer. Math. Soc.
**21**(1989), 71-75

- $AD$ and the very fine structure of $L\left ( \mathbb {R} \right )$
- Steve Jackson PDF
- Bull. Amer. Math. Soc.
**21**(1989), 77-81

- Eta-invariants and von Neumann algebras
- R. G. Douglas, S. Hurder and J. Kaminker PDF
- Bull. Amer. Math. Soc.
**21**(1989), 83-87

- A nonvanishing theorem for derivatives of automorphic $L$-functions with applications to elliptic curves
- Daniel Bump, Solomon Friedberg and Jeffrey Hoffstein PDF
- Bull. Amer. Math. Soc.
**21**(1989), 89-93

##
Book Reviews

Book reviews do not contain an abstract. You may
download each review in this issue using the links
below.

- Class field theory, by Jürgen Neukirch.
- Local class field theory, by Kenkichi Iwasawa.
- Reviewer: Michiel Hazewinkel

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 95-101

- Multiphase averaging for classical systems, with applications to adiabatic theorems, by Pierre Lochak and Claude Meunier.
- Reviewer: Philip Holmes

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 101-105

- Spectral theory of linear differential operators and comparison algebras, by H. O. Cordes.
- Reviewer: Alexander Dynin

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 105-108

- Iwasawa theory of elliptic curves with complex multiplication, by Ehud de Shalit.
- Reviewer: Karl Rubin

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 108-112

- Ergodic theory of random transformations, by Yuri Kifer.
- Reviewer: Peter Walters

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 113-117

- The homotopy index and partial differential equations, by Krzysztof P. Rybakowski.
- Reviewer: Jean Mawhin

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 118-121

- Quadratic and Hermitian forms, by Winfried Scharlau.
- Reviewer: T. Y. Lam

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 121-125

- Collected mathematical papers of Jacob Nielson, by Vagn Lundsgaard Hansen.
- Reviewer: Jane Gilman

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 125-129

- Basic hypergeometric series and applications, by Nathan J. Fine.
- Reviewer: Richard Askey

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 130-132

- Stationary sequences and random fields, by Murray Rosenblatt.
- Reviewer: G. Kallianpur

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 133-139

- Free rings and their relations, by P. M. Cohn.
- Reviewer: Jacques Lewin

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 139-142

- Sphere packings, lattices and groups, by J. H. Conway and N. J. A. Sloane.
- Reviewer: Richard K. Guy

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 142-147

- Foundations of analysis over surreal number fields, by N. L. Alling.
- Reviewer: P. M. Cohn

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 148-149

- Theory of topological structures. An approach to categorical topology, by Gerhard Preuss.
- Reviewer: Walter Tholen

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 149-152

- Multidimensional Brownian excursions and potential theory, by K. Burdzy.
- Reviewer: Thomas S. Salisbury

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 152-157

- Riemannian geometry, by S. Gallot, D. Hulin and J. Lafontaine.
- Reviewer: Robert E. Greene

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 157-162

- The complex analytic theory of Teichmüller spaces, by Subhashis Nag.
- Reviewer: William Abikoff

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 162-168

- Extensions and absolutes of Hausdorff spaces, by JackR. Porter and R. Grant Woods.
- Reviewer: Melvin Henriksen

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 168-171

- Introduction to Arakelov theory, by Serge Lang.
- Reviewer: Joseph H. Silverman

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 171-176

- Calculus on Heisenberg manifolds, by Richard Beals and Peter Greiner.
- Reviewer: Nancy K. Stanton

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 177-179

- An introduction to independence for analysts, by H. G. Dales and W. H. Woodin.
- Reviewer: M. Alain Louveau

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 179-181

- Random polynomials, by A. T. Bharucha-Reid and M. Sambandham.
- Reviewer: G. Samal

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 182-183

- $H^\infty$ Operator theory and arithmetic in, by Hari Bercovici.
- Reviewer: Pei Yuan Wu

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 184-186

- Stratified Morse theory, by M. Goresky and R. MacPherson.
- Reviewer: K.-H. Fieseler

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 186-188

- Introduction to superanalysis, by Felix Alexandrovich Berezin.
- Reviewer: Mitchell J. Rothstein

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 189-192

- Gauge field theory and complex geometry, by Yuri I. Manin.
- Reviewer: Claude Lebrun

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 192-196

- Infinite-dimensional dynamical systems in mechanics and physics, by Roger Temam.
- Reviewer: John Guckenheimer

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 196-198

- Orthogonality and spacetime geometry, by Robert Goldblatt.
- Reviewers: A. D. Taimanov and Alexander K. Guts

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 199-200

- Partially ordered abelian groups with interpolation, by K. R. Goodearl.
- Reviewer: George A. Elliott

- Review information PDF
- Bull. Amer. Math. Soc.
**21**(1989), 200-204