Number Theory and Modular Forms: Papers in Memory of Robert A. Rankin

Front Matter....Pages i-8
The Life and Work of R.A. Rankin (1915–2001)....Pages 9-38
Memoir: My Cambridge Years....Pages 39-42
The De Morgan Medal....Pages 43-44
On the Petersson Norm of Certain Siegel Modular Forms....Pages 45-48
On Borcherds Products Associated with Lattices of Prime Discriminant....Pages 49-61
An L -Function of Degree 27 for Spin 9 ....Pages 63-78
Representations of Integers as Sums of 32 Squares....Pages 79-89
Some Remarks on Signs in Functional Equations....Pages 91-93
On Dirichlet Series for Sums of Squares....Pages 95-127
Poincaré Series and Hilbert Modular Forms....Pages 129-140
On Non-Congruence Subgroups of the Analogue of the Modular Group in Characteristic p ....Pages 141-144
On Modular Forms Arising from a Differential Equation of Hypergeometric Type....Pages 145-164
A Note on Base Change, Identities Involving τ ( n ), and a Congruence of Ramanujan....Pages 165-168
The Orders of Related Elements of a Finite Field....Pages 169-183
On the Uniform Distribution of Certain Sequences....Pages 185-192
Modular Transformations of Ramanujan’s Fifth and Seventh Order Mock Theta Functions....Pages 193-222
Estimates for Sums of Coefficients of Dirichlet Series with Functional Equation....Pages 223-233
Rational Points on the Sphere....Pages 235-239
Estimating Additive Character Sums for Fuchsian Groups....Pages 241-267
On the Signs of Fourier Coefficients of Cusp Forms....Pages 269-277
On the Asymptotic Behaviour of General Partition Functions, II....Pages 279-298
More Primes and Polynomials....Pages 299-320
On the Generalized Rogers-Ramanujan Continued Fraction....Pages 321-331
On the Parity of the Number of Partitions in Square Free Parts....Pages 333-341
Relations Between the Ranks and Cranks of Partitions....Pages 343-366
Perspectives de l’Approximation Diophantienne et de la Transcendance....Pages 367-384
Partitions: At the Interface of q -Series and Modular Forms....Pages 385-400