# The Ramanujan Journal

The Ramanujan Journal > 1997 > 1 > 1 > 7-23

The Ramanujan Journal > 1997 > 1 > 1 > 75-90

*H(q)*. These include relations between

*H(q)*and

*H(q*

^{ n }) , which are established using modular equations of degree

*n*. We also evaluate explicitly

*H(q)*at $$q = e^{ - \pi \sqrt n /2} $$ for various positive integers

*n*. Using results of M. Deuring, we show that $$H( \pm e^{ - \pi \sqrt n /2} ) $$ are...

The Ramanujan Journal > 1997 > 1 > 1 > 25-34

*k*and let

*b*

_{k}

*(n)*denote the number of partitions of a non-negative integer

*n*into parts none of which are multiples of

*k*. If

*M*is a positive integer, let

*S*

_{k}

*(N; M)*be the number of positive integers ≤

*N*for which

*b*

_{k}(

*n*...

The Ramanujan Journal > 1997 > 1 > 1 > 101-111

*N*into distinct parts is equal to the number of partitions of

*N*into odd parts. Our version says that the number of “lecture hall partitions of length

*n*” of

*N*equals the number of partitions of

*N*into small odd parts: 1,3,5, ldots, 2

*n*-1 . We give two proofs: one via Bott's formula for the Poincaré...

The Ramanujan Journal > 1997 > 1 > 1 > 35-52

The Ramanujan Journal > 1997 > 1 > 1 > 53-74

The Ramanujan Journal > 1997 > 1 > 1 > 91-99

The Ramanujan Journal > 1997 > 1 > 2 > 119-153

The Ramanujan Journal > 1997 > 1 > 2 > 187-210

The Ramanujan Journal > 1997 > 1 > 2 > 155-163

^{3}. An axis of a hyperbolic element of Γ(1) projects to a simple closed geodesic on one of these surfaces if and only if it does so on the other two. This equivalence was...

The Ramanujan Journal > 1997 > 1 > 2 > 165-185

_{1},...,a

_{n}) we define L

_{a}to be the set of n-tuples of integers λ = (λ

_{1},...,λ

_{n}) satisfying $$0 \leqslant \frac{{\lambda _{\text{1}} }}{{a_1 }} \leqslant \frac{{\lambda _2 }}{{a_2 }} \leqslant \cdots \leqslant \frac{{\lambda _n }}{{a_n }}$$ . This generalizes the so-called lecture hall partitions corresponding to a

_{i}=i and previously studied by the authors...

The Ramanujan Journal > 1997 > 1 > 2 > 211-220

The Ramanujan Journal > 1997 > 1 > 3 > 309-322

The Ramanujan Journal > 1997 > 1 > 3 > 275-297

The Ramanujan Journal > 1997 > 1 > 3 > 227-241

The Ramanujan Journal > 1997 > 1 > 3 > 299-308

The Ramanujan Journal > 1997 > 1 > 3 > 243-274

The Ramanujan Journal > 1997 > 1 > 4 > 339-350

The Ramanujan Journal > 1997 > 1 > 4 > 333-337

The Ramanujan Journal > 1997 > 1 > 4 > 363-378