Contents

Preface vii

Program for q-series piano recital ix

Congruences and conjectures for the partition function

S. AHLGREN AND

K.

0NO

1

MacMahon's partition analysis VII: Constrained compositions

G. E.

ANDREWS, P. PAULE, AND A. RIESE

11

Crystal bases and q-identities

M.

0KADO, A. SCHILLING AND

M.

SHIMOZONO

29

The Bailey-Rogers-Ramanujan group

D

0

STANTON

55

Multiple polylogarithms: A brief survey

D.

BOWMAN AND

D. M.

BRADLEY

71

Swinnerton-Dyer type congruences for certain Eisenstein series

M.

BOYLAN

93

More generating functions for L-function values

G. G. H.

CooGAN

109

On sums of an even number of squares, and an even number of

triangular numbers: an elementary approach based on Ramanujan's

1

'lj;1 summation formula

S. COOPER

115

Some remarks on multiple Sears transformations

Y.

KAJIHARA

139

Another way to count colored Frobenius partitions

L. W.

KOLITSCH

147

Proof of a summation formula for an

An

basic hypergeometric series

conjectured by Warnaar

C. KRATTENTHALER

153

On the representation of integers as sums of squares

Z.-G. Lru

163

v