ΤΑΥΤΟΠΟΙΗΣΙΣ TΩN ΤΥΠΩΝ Β, C ΚΑΙ D TOY ΓΕΝΟΥΣ WELCHIA ΔIA TOY ΠΡΟΣΔΙΟΡΙΣΜΟΥ ΤΗΣ ΑΝΤΙΓΟΝΙΚΗΣ ΣΥΝΘΕΣΕΩΣ ΑΥΤΩΝ

Toy Models for D. H. Lehmer’s Conjecture

In 1947, Lehmer conjectured that the Ramanujan τ -function τ(m) never vanishes for all positive integers m, where the τ(m) are the Fourier coefficients of the cusp form ∆24 of weight 12. Lehmer verified the conjecture in 1947 for m < 214928639999. In 1973, Serre verified up to m < 10, and in 1999, Jordan and Kelly for m < 22689242781695999. The theory of spherical t-design, and in particular th...

Far From Toy Trains

Toy Models for Retrocausality

A number of writers have been attracted to the idea that some of the peculiarities ofquantum theory might be manifestations of ‘backward’ or ‘retro’ causality, underlying thequantum description. This idea has been explored in the literature in two main ways:firstly in a variety of explicit models of quantum systems, and secondly at a concep-tual level. This note introduces a...

Weighted Supermembrane Toy Model

A weighted Hilbert space approach to the study of zero-energy states of supersymmetric matrix models is introduced. Applied to a related but technically simpler model, it is shown that the spectrum of the corresponding weighted Hamiltonian simplifies to become purely discrete for sufficient weights. This follows from a bound for the number of negative eigenvalues of an associated matrix-valued ...

On Toy Aging

We consider the dynamics of a simple one dimensional model and we discuss the phenomenon of aging (i.e., the strong dependence of the dynamical correlation functions over the waiting time). Our model is the so-called random random walk, the toy model of a directed polymer evolving in a random medium. ROMA LA SAPIENZA 962-93, cond-mat/9308003