6,658 research outputs found
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
The Balanced Scorecard: translating strategy into results
In the paper it is shown that the Balanced Business Scorecard (BSC) allows a balance between financial and non financial objectives and performs a quantification of the dimensions of strategy in four areas - financial, customers, processes and potential. Moreover, the BSC provides feedback on internal processes and external outcomes in order to improve further the performance and results in terms of strategy. When the Balanced Scorecard is implemented effectively, can transform strategic planning from an academic exercise in the central nervous of the entire company.strategy, financial objectives, non financial objectives, Balanced Business Scorecard, performance measurement
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