Lord Atkin of Aberdovey

On Atkin

In this paper we give an example of a noncongruence subgroup whose three-dimensional space of cusp forms of weight 3 has the following properties. For each of the four residue classes of odd primes modulo 8 there is a basis whose Fourier coefficients at infinity satisfy a three-term Atkin and Swinnerton-Dyer congruence relation, which is the p-adic analogue of the threeterm recursion satisfied ...

On a Conjecture of Atkin

Let j be the modular invariant. For the primes p ≤ 23 the q-expansion coefficients of U(j− 744) are multiplicative as it was a Hecke eigenformmodulo a power of p which increases withm. This was conjectured by Atkin on the basis of extensive numerical experiments, and is proved in this paper. The cases p = 5, 7 and 11 are under special consideration in this paper.

Lord Lister

i hp; medical man who wishes to gain a clear idea of the broad foundations upon which modern medicine and surgery are based should read two great books which are almost twin classics; Rene Vallery Radot's Life of Pasteur" (English translation by Mrs. Devonshire), and Sir Rickman Godlee's "Lord Lister," the re-appearance of which in a third edition we cordially welcome. Both are finely written s...

On a Result of Atkin and Lehner

We wish to give a new proof of one of the main results of Atkin-Lehner [1]. That paper depends, among other things, on a slightly strengthened version of Theorem 1 below, which characterizes forms in Sk(Γ0(N)) whose Fourier coefficients satisfy a certain vanishing condition. Our proof involves rephrasing this vanishing condition in terms of representation theory; this, together with an elementa...

The Gardens of the Lord