Mr. Dyer on Physiological Selection

On Atkin and Swinnerton - Dyer Congruence

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 ...

Mr. Good's System of Physiological Nosology

The Birch-swinnerton-dyer Conjecture

We give a brief description of the Birch-Swinnerton-Dyer conjecture which is one of the seven Clay problems.

Split Dual Dyer-Lashof Operations

For each admissible monomial of Dyer-Lashof operations QI , we define a corresponding natural function Q̂I :TH̄∗(X) → H ∗(ΩnΣnX), called a Dyer-Lashof splitting. For every homogeneous class x in H∗(X), a Dyer-Lashof splitting Q̂I determines a canonical element y in H∗(ΩnΣnX) so that y is connected to x by the dual homomorphism to the operation QI . The sum of the images of all the admissible Dyer-...

On Atkin and Swinnerton-dyer Congruence Relations (3)

In the previous two papers with the same title ([LLY05] by W.C. Li, L. Long, Z. Yang and [ALL05] by A.O.L. Atkin, W.C. Li, L. Long), the authors have studied special families of cuspforms for noncongruence arithmetic subgroups. It was found that the Fourier coefficients of these modular forms at infinity satisfy three-term Atkin and Swinnerton-Dyer congruence relations which are the p-adic anal...