14,761 research outputs found
Integrals on -adic upper half planes and Hida families over totally real fields
Bertolini-Darmon and Mok proved a formula of the second derivative of the
two-variable -adic -function of a modular elliptic curve over a totally
real field along the Hida family in terms of the image of a global point by
some -adic logarithm map. The theory of -adic indefinite integrals and
-adic multiplicative integrals on -adic upper half planes plays an
important role in their work. In this paper, we generalize these integrals for
-adic measures which are not necessarily -valued, and prove a
formula of the second derivative of the two-variable -adic -function of
an abelian variety of -type associated to a Hilbert modular form
of weight 2.Comment: to appear in Osaka Journal of Mathematic
Some Properties of String Field Algebra
We examine string field algebra which is generated by star product in
Witten's string field theory including ghost part. We perform calculations
using oscillator representation consistently. We construct wedge like states in
ghost part and investigate algebras among them. As a by-product we have
obtained some solutions of vacuum string field theory. We also discuss some
problems about identity state. We hope these calculations will be useful for
further investigation of Witten type string field theory.Comment: 26 pages, typos corrected, v3:Eq.(92) corrected, v4:to be published
in JHE
Scanning Multivariate Conditional Densities with Probability Integral Transforms
This paper introduces new ways to construct probability integral transforms of random vectors that complement the approach of Diebold, Hahn, and Tay (1999) for evaluating multivariate conditional density forecasts. Our approach enables us to "scan" multivariate densities in various di.erent ways. A simple bivariate normal example is given that illustrates how "scanning" a multivariate density from particular angles leads to tests with no power or high power. An empirical example is also given that applies several di.erent probability integral transforms to specification testing of Engle's (2002) dynamic conditional correlation model for multivariate financial returns time series with multivariate normal and t errors.
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