2,846 research outputs found
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
and , 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 : we determine explicit trace forms for
with Nebentypus, and we compute the limit of the trace of a fixed
Hecke operator as the level 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
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