Improving the Partial-Global Stochastic Metropolis Update for Dynamical Smeared Link Fermions

We discuss several methods that improve the partial-global stochastic Metropolis (PGSM) algorithm for smeared link staggered fermions. We present autocorrelation time measurements and argue that this update is feasible even on reasonably large lattices.Comment: 3 pages, 3 figures, Lattice2002(algor

On the trace formula for Hecke operators on congruence subgroups, II

In a previous paper, we obtained a general trace formula for double coset operators acting on modular forms for congruence subgroups, expressed as a sum over conjugacy classes. Here we specialize it to the congruence subgroups $\Gamma_0(N)$ and $\Gamma_1(N)$, obtaining explicit formulas in terms of class numbers for the trace of a composition of Hecke and Atkin-Lehner operators. The formulas are among the simplest in the literature, and hold without any restriction on the index of the operators. We give two applications of the trace formula for $\Gamma_1(N)$: we determine explicit trace forms for $\Gamma_0(4)$ with Nebentypus, and we compute the limit of the trace of a fixed Hecke operator as the level $N$ tends to infinity

An algebraic property of Hecke operators and two indefinite theta series

We prove an algebraic property of the elements defining Hecke operators on period polynomials associated with modular forms, which implies that the pairing on period polynomials corresponding to the Petersson scalar product of modular forms is Hecke equivariant. As a consequence of this proof, we derive two indefinite theta series identities which can be seen as analogues of Jacobi's formula for the theta series associated with the sum of four squares.Comment: 11 pages. Published version. Forum Math., published online February 201