Transactions of the American Mathematical Society

We discuss a generalization of partitions, called overpartitions, which have proven useful in several combinatorial studies of basic hypergeometric series. After showing how a number of finite products occurring in q-series have natural interpretations in terms of overpartitions, we present an introduction to their rich structure as revealed by q-series identities.

[1]  Linear systems of curves upon algebraic surfaces , 1903 .

[2]  J. Dieudonne,et al.  On the automorphisms of the classical groups. With a supplement by Loo-Keng Hua , 1951 .

[3]  ON REPRESENTATIONS AND EXTENSIONS OF BOUNDED LINEAR FUNCTIONALS DEFINED ON CLASSES OF ANALYTIC FUNCTIONS , 1954 .

[4]  J. Roth.  Algebraic topological methods for the synthesis of switching systems. I , 1958 .

[5]  The Hausdorff-Besicovich Dimension of the Level Sets of Person's Modular Function , 1966 .

[6]  Stefan Rolewicz,et al.  On a problem of moments , 1968 .

[7]  A. Aziz,et al.  Periodic solutions of hyperbolic partial differential equations in a strip , 1969 .

[8]  S. Tanaka,et al.  ON AN EXPLICIT CONSTRUCTION OF A CERTAIN CLASS OF AUTOMORPHIC FORMS. , 1969 .

[9]  A class of translation planes and a conjecture of D. R. Hughes , 1969 .

[10]  George E. Andrews,et al.  On a calculus of partition functions , 1969 .

[11]  R. Blattner.  Induced and produced representations of Lie algebras , 1969 .

[12]  A. Varma,et al.  An analogue of a problem of J. Balázs and P. Turán, II (Inequalities) , 1970 .

[13]  G. Webb.  Nonlinear evolution equations and product integration in Banach spaces. , 1970 .

[14]  Automorphic Forms on GL(2) , 1970 .

[15]  L. Goldstein.  A generalization of the Siegel-Walfisz theorem , 1970 .

[16]  Generalizations of the Durfee Square , 1971 .

[17]  Hervé Jacquet.  Automorphic Forms on GL(2) Part II , 1972 .

[18]  Harry Lakser,et al.  The structure of pseudocomplemented distributive lattices. III. Injective and absolute subretracts , 1972 .

[19]  Richard Askey,et al.  Theory and Application of Special Functions , 1975 .

[20]  George E. Andrews,et al.  Problems and Prospects for Basic Hypergeometric Functions , 1975 .

[21]  R. Langlands.  On the Functional Equations Satisfied by Eisenstein Series , 1976 .

[22]  REPRESENTATIONS OF THE GROUP GL(n, F) WHERE F IS A NON-ARCHIMEDEAN LOCAL FIELD , 1976 .

[23]  J. Arthur.  Eisenstein series and the trace formula , 1977 .

[24]  T. Asai.  On certain Dirichlet series associated with Hilbert modular forms and Rankin's method , 1977 .

[25]  Allan G. Silberger,et al.  Introduction to Harmonic Analysis on Reductive P-adic Groups. , 1979 .

[26]  G. Andrews.  PARTITIONS AND DURFEE DISSECTION. , 1979 .

[27]  Keisuke Uchimura,et al.  An Identity for the Divisor Generating Function Arising from Sorting Theory , 1981, J. Comb. Theory, Ser. A.

[28]  George E. Andrews,et al.  Ramanujan's “Lost” Notebook. I. Partial θ-functions , 1981 .

[29]  F. Shahidi.  On Certain L-Functions , 1981 .

[30]  P. Perrin.  Representations de Schrödinger Indice de Maslov et groupe metaplectique , 1981 .

[31]  Hervé Jacquet.  On the residual spectrum of GL(n) , 1983 .

[32]  D. Bressoud,et al.  On Uchimura’s Connection between Partitions and the Number of Divisors , 1984, Canadian Mathematical Bulletin.

[33]  Emil Grosswald,et al.  The Theory of Partitions , 1984 .

[34]  George E. Andrews,et al.  Generalized Frobenius Partitions , 1984 .

[35]  G. Harder,et al.  Algebraische Zyklen auf Hilbert-Blumenthal-Flächen. , 1986 .

[36]  D. Vogan.  The unitary dual of GL(n) over an archimedean field , 1986 .

[37]  M. Vignéras,et al.  Correspondances de Howe sur un corps p-adique , 1987 .

[38]  S. Rallis.  L-Functions and the Oscillator Representation , 1987 .

[39]  Dennis Stanton,et al.  Bijective proofs of basic hypergeometric series identities , 1987 .

[40]  Ramanujan's lost notebook , 1987 .

[41]  F. Shahidi,et al.  Artin $L$-functions and normalization of intertwining operators , 1988 .

[42]  N. J. Fine,et al.  Basic Hypergeometric Series and Applications , 1988 .

[43]  F. Dyson,et al.  Partitions and indefinite quadratic forms , 1988 .

[44]  Y. Ye.  Kloosterman integrals and base change for GL (2). , 1989 .

[45]  J. Arthur.  Intertwining operators and residues I. Weighted characters , 1989 .

[46]  Y. Flicker.  On distinguished representations. , 1991 .

[47]  S. Kudla,et al.  On the degree 5L-function for Sp(2) , 1992 .

[48]  S. Kudla.  Splitting metaplectic covers of dual reductive pairs , 1994 .

[49]  Some results on reducibilty for unitary groups and local Asai L-functions. , 1994 .

[50]  C. Mœglin,et al.  Décomposition spectrale et séries d'Eisenstein : une paraphrase de l'écriture , 1994 .

[51]  T. Ikeda.  On the theory of Jacobi forms and Fourier-Jacobi coefficients of Eisenstein series , 1994 .

[52]  Soo Teck Lee.  On Some Degenerate Principal Series Representations of U(n,n) , 1994 .

[53]  Henry H. Kim.  The residual spectrum of $Sp_4$ , 1995 .

[54]  Soo Teck Lee,et al.  Degenerate principal series and local theta correspondence , 1998 .

[55]  A. Borel,et al.  Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups , 1999 .

[56]  Krishnaswami Alladi,et al.  A Fundamental Invariant in the Theory of Partitions , 1999 .