Edited by: Yuri Lyubich et al.
Entire Functions in Modern Analysis
: Boris Levin Memorial Conference
Expected publication date is January 4, 2002
Description
This volume presents the proceedings from the conference, "Entire Functions in Modern Analysis" held at Tel-Aviv University (Ramat-Aviv, Israel) in memory of Professor Boris Levin, an outstanding mathematician and a brilliant teacher whose mathematical activity spanned over 60 years. Levin's scientific interests lay principally in the theory of analytic functions and its applications to harmonic analysis, functional analysis, and operator theory. His ideas and results in this area, as expressed both through his personal influence and his papers and books, have influenced several generations of mathematicians.
Contents
A. Aleman, H. Hedenmalm, S. Richter, and C. Sundberg -- Curious properties of canonical divisors in weighted Bergman spaces
N. Arakelian and A. Hakobian -- Entire functions with infinite sets of deficient functions
V. Azarin and D. Drasin -- A generalization of completely regular growth
G. Belitskii, E. Dyn'kin, and V. Tkachenko -- Difference equations in Carleman classes
R. Brooks and E. Makover -- Belyi surfaces
A. Brudnyi -- Inequalities for entire functions
S. Yu. Favorov, A. Yu. Rashkovskii, and L. I. Ronkin -- Almost periodic currents, chains and divisors in tube domains
B. Freydin -- On spectral synthesis of polynomially growing functions on a half-axis
A. Fryntov and J. Rossi -- Hyperbolic symmetrization and an inequality of Dyn'kin
M. Girnyk and A. Goldberg -- Approximation of subharmonic functions by logarithms of moduli of entire functions in integral metrics
A. F. Grishin and T. I. Malyutina -- Subharmonic functions satisfying the local Levin condition
V. P. Havin and A. H. Nersessian -- Bounded separation of singularities of analytic functions
O. M. Katkova and A. M. Vishnyakova -- Zeros sets of entire absolutely monotonic functions
B. N. Khabibullin -- Dual approach to certain questions for weighted spaces of holomorphic functions
S. L. Krushkal -- Quasiconformal reflections and mirrors
Y. Lyubarskii and K. Seip -- A splitting problem for unconditional bases of complex exponentials
V. Matsaev and M. Sodin -- Entire functions and compact operators with S_p-imaginary component
V. V. Napalkov, Jr. and R. S. Youlmukhametov -- Criterion of surjectivity of the Cauchy transform operator on a Bergman space
M. Novitskii and Yu. Safarov -- Periodic points of quasianalytic Hamiltonian billiards
A. Olevskii -- Change of variable in Fourier expansions: Some old and new results
I. V. Ostrovskii -- On zero distribution of sections and tails of power series
R. Rocha-Chavez and M. Shapiro -- On singular integrals of the time-harmonic relativistic Dirac bispinors theory
N. Roytvarf -- Generalized moments, composition of polynomials and Bernstein classes
N. Skiba and V. Zahariuta -- Bernstein-Walsh theorems for harmonic functions in R^n
A. Ulanovskii -- Measures whose supports do not have periodic holes
Details:
Series: Israel Mathematical Conference Proceedings, Volume: 15
Publication Year: 2002
ISBN: 1-000-01570-X
Paging: 392 pp.
Binding: Softcover
Edited by: John McKay, Concordia University, Montreal, PQ, Canada,
and Abdellah Sebbar, University of Ottawa, ON, Canada
Proceedings on Moonshine and Related Topics
Description
This volume contains the proceedings of the Moonshine workshop held at the Centre de Recherches Mathematiques (CRM) in Montreal. A glance at the contents will reveal that the connection of some papers to Moonshine is not immediate; however, Moonshine has proved to be a very fertile area, and it does not stretch the imagination to believe that many more threads will be drawn together before we understand what is really going on.
In this volume, all the classical Moonshine themes are presented, namely the Monster simple group and other finite groups, automorphic functions and forms and related congruence groups, and vertex algebras and their representations. These topics appear in either a pure form or in a blend of algebraic geometry dealing with algebraic surfaces, Picard-Fuchs equations, and hypergeometric functions.
Contents
A. Baker and H. Tamanoi -- Invariants for finite dimensional groups in vertex operator algebras associated to basic representations of affine algebras
C. Dong and G. Mason -- Transformation laws for theta functions
C. F. Doran -- Algebro-geometric isomonodromic deformations linking Hauptmoduls: Variation of the mirror map
G. Glauberman and S. P. Norton -- On McKay's connection between the affine E_8 diagram and the monster
K. Harada and M. L. Lang -- Sylow 2-subgroups of simple groups
W. L. Hoyt and C. F. Schwartz -- Yoshida surfaces with Picard number \rho \geq 17
M. Kaneko and N. Todaka -- Hypergeometric modular forms and supersingular elliptic curves
C. H. Lam -- Fusion rules for ternary and \mathbb{Z}_2 \times \mathbb{Z}_2 code vertex operator algebras
H. Li -- The regular representations and the A_{n}(V)-algebras
J. McKay -- Linear dependencies among completely replicable functions
J. McKay and A. Sebbar -- Arithmetic semistable elliptic surfaces
M. Miyamoto -- Modular invariance of trace functions on VOAs in many variables
N. Narumiya and H. Shiga -- The mirror map for a family of K3 surfaces induced from the simplest 3-dimensional reflexive polytope
S. Norton -- From moonshine to the monster
Y. Ohyama -- Hypergeometric functions and non-associative algebras
K. Saito -- Extended affine root systems. V. Elliptic eta-products and their Dirichlet series
C. S. Simons -- Deflating infinite Coxeter groups to finite groups
M. P. Tuite -- Genus two meromorphic conformal field theory
H. Verrill -- Picard-Fuchs equations of some families of elliptic curves
Details:
Series: CRM Proceedings & Lecture Notes,Volume: 30
Publication Year: 2001
ISBN: 0-8218-2879-7
Paging: 268 pp.
Binding: Softcover
Edited by: Bruce C. Berndt, University of Illinois, Urbana, IL,
and Ken Ono, University of Wisconsin, Madison, WI
q-Series with Applications to Combinatorics,
Number Theory, and Physics
Description
The subject of q-series can be said to begin with Euler and his pentagonal number theorem. In fact, q-series are sometimes called Eulerian series. Contributions were made by Gauss, Jacobi, and Cauchy, but the first attempt at a systematic development, especially from the point of view of studying series with the products in the summands, was made by E. Heine in 1847. In the latter part of the nineteenth and in the early part of the twentieth centuries, two English mathematicians, L. J. Rogers and F. H. Jackson, made fundamental contributions.
In 1940, G. H. Hardy described what we now call Ramanujan's famous _1\psi_1 summation theorem as "a remarkable formula with many parameters." This is now one of the fundamental theorems of the subject.
Despite humble beginnings, the subject of q-series has flourished in the past three decades, particularly with its applications to combinatorics, number theory, and physics. During the year 2000, the University of Illinois embraced The Millennial Year in Number Theory. One of the events that year was the conference q-Series with Applications to Combinatorics, Number Theory, and Physics. This event gathered mathematicians from the world over to lecture and discuss their research.
This volume presents nineteen of the papers presented at the conference. The excellent lectures that are included chart pathways into the future and survey the numerous applications of q-series to combinatorics, number theory, and physics.
Contents
B. C. Berndt and K. Ono -- q-series Piano recital: Levis faculty center
Congruences and conjectures for the partition function
MacMahon's partition analysis VII: Constrained compositions
Crystal bases and q-identities
The Bailey-Rogers-Ramanujan group
Multiple polylogarithms: A brief survey
Swinnerton-Dyer type congruences for certain Eisenstein series
More generating functions for L-function values
On sums of an even number of squares, and an even number of triangular numbers: An elementary approach based on Ramanujan's _1\psi_1 summation formula
Some remarks on multiple Sears transformations
Another way to count colored Frobenius partitions
Proof of a summation formula for an \tilde A_n basic hypergeometric series conjectured by Warnaar
On the representation of integers as sums of squares
3-regular partitions and a modular K3 surface
A new look at Hecke's indefinite theta series
A proof of a multivariable elliptic summation formula conjectured by Warnaar
Multilateral transformations of q-series with quotients of parameters that are nonnegative integral powers of q
Completeness of basic trigonometric system in \mathcal{L}^{p}
The generalized Borwein conjecture. I. The Burge transform
Mock \vartheta-functions and real analytic modular forms
Details:
Series: Contemporary Mathematics, Volume: 291
Publication Year: 2001
ISBN: 0-8218-2746-4
Paging: 277 pp.
Binding: Softcover
Jose I. Burgos Gil, Universidad de Barcelona, Spain
The Regulators of Beilinson and Borel
Description
This book contains a complete proof of the fact that Borel's regulator map is twice Beilinson's regulator map. The strategy of the proof follows the argument sketched in Beilinson's original paper and relies on very similar descriptions of the Chern-Weil morphisms and the van Est isomorphism.
The book has two different parts. The first one reviews the material from algebraic topology and Lie group theory needed for the comparison theorem. Topics such as simplicial objects, Hopf algebras, characteristic classes, the Weil algebra, Bott's Periodicity theorem, Lie algebra cohomology, continuous group cohomology and the van Est Theorem are discussed.
The second part contains the comparison theorem and the specific material needed in its proof, such as explicit descriptions of the Chern-Weil morphism and the van Est isomorphisms, a discussion about small cosimplicial algebras, and a comparison of different definitions of Borel's regulator.
Contents
Introduction
Simplicial and cosimplicial objects
H-spaces and Hopf algebras
The cohomology of the general linear group
Lie algebra cohomology and the Weil algebra
Group cohomology and the van Est isomorphism
Small cosimplicial algebras
Higher diagonals and differential forms
Borel's regulator
Beilinson's regulator
Bibliography
Index
Details:
Series: CRM Monograph Series,Volume: 15
Publication Year: 2002
ISBN: 0-8218-2630-1
Paging: approximately 120 pp.
Binding: Hardcover