170 research outputs found
Constructing vector-valued Siegel modular forms from scalar-valued Siegel modular forms
This paper gives a simple method for constructing vector-valued Siegel
modular forms from scalar-valued ones. The method is efficient in producing the
siblings of Delta, the smallest weight cusp forms that appear in low degrees.
It also shows the strong relations between these modular forms of different
genera. We illustrate this by a number of examples.Comment: 21 pages; misprints corrected; to appear in PAM
Siegel modular forms of genus 2 and level 2
We study vector-valued Siegel modular forms of genus 2 and level 2. We
describe the structure of certain modules of vector-valued modular forms over
rings of scalar-valued modular forms.Comment: 46 pages. To appear in International Journal of Mathematic
Covariants of binary sextics and vector-valued Siegel modular forms of genus two
We extend Igusa's description of the relation between invariants of binary
sextics and Siegel modular forms of degree two to a relation between covariants
and vector-valued Siegel modular forms of degree two. We show how this relation
can be used to effectively calculate the Fourier expansions of Siegel modular
forms of degree two.Comment: 19 page
Modeling the Temperature Bias of Power Consumption for Nanometer-Scale CPUs in Application Processors
We introduce and experimentally validate a new macro-level model of the CPU
temperature/power relationship within nanometer-scale application processors or
system-on-chips. By adopting a holistic view, this model is able to take into
account many of the physical effects that occur within such systems. Together
with two algorithms described in the paper, our results can be used, for
instance by engineers designing power or thermal management units, to cancel
the temperature-induced bias on power measurements. This will help them gather
temperature-neutral power data while running multiple instance of their
benchmarks. Also power requirements and system failure rates can be decreased
by controlling the CPU's thermal behavior.
Even though it is usually assumed that the temperature/power relationship is
exponentially related, there is however a lack of publicly available physical
temperature/power measurements to back up this assumption, something our paper
corrects. Via measurements on two pertinent platforms sporting nanometer-scale
application processors, we show that the power/temperature relationship is
indeed very likely exponential over a 20{\deg}C to 85{\deg}C temperature range.
Our data suggest that, for application processors operating between 20{\deg}C
and 50{\deg}C, a quadratic model is still accurate and a linear approximation
is acceptable.Comment: Submitted to SAMOS 2014; International Conference on Embedded
Computer Systems: Architectures, Modeling, and Simulation (SAMOS XIV
Covariants of binary sextics and modular forms of degree 2 with character
We use covariants of binary sextics to describe the structure of modules of
scalar-valued or vector-valued Siegel modular forms of degree 2 with character,
over the ring of scalar-valued Siegel modular forms of even weight. For a
modular form defined by a covariant we express the order of vanishing along the
locus of products of elliptic curves in terms of the covariant.Comment: 18 page
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