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Index theory for basic Dirac operators on Riemannian foliations

, 2010
In this paper we prove a formula for the analytic index of a basic Dirac-type operator on a Riemannian foliation, solving a problem that has been open for many years.
Bressler, Paul +3 more
core +1 more source

Realizing Scale-invariant Density Perturbations in Low-energy Effective String Theory

, 2007
We discuss the realization of inflation and resulting cosmological perturbations in the low-energy effective string theory. In order to obtain nearly scale-invariant spectra of density perturbations and a suppressed tensor-to-scalar ratio, it is ...
A. Linde +8 more
core +1 more source

The expansion of a finite number of terms of the Gauss hypergeometric function of unit argument and the Landau constants [PDF]

, 2014
We obtain convergent inverse factorial expansions for the sum Sn(a, b; c) of the first n ≥ 1 terms of the Gauss hypergeometric function 2F1(a, b; c; 1) of unit argument. The form of these expansions depends on the location of the parametric excess s := c−
Paris, R. B.
core +2 more sources

Local units and Gauss sums

Journal of Number Theory, 2003
Let \(F\) be an abelian number field containing a primitive root of unity \(\zeta _ p\) with Galois group \(\Lambda = {\text{Gal}} (F/{\mathbb Q})\) over \(\mathbb Q\). For a fixed prime number \(p\), let \(F _ \infty\) denote the cyclotomic \({\mathbb Z} _ p\) extension of \(F\), where \({\mathbb Z}_ p\) denotes the ring of \(p\)-adic numbers.
openaire +1 more source

On Classical Gauss Sums and Some of Their Properties [PDF]

Symmetry, 2018
The goal of this paper is to solve the computational problem of one kind rational polynomials of classical Gauss sums, applying the analytic means and the properties of the character sums. Finally, we will calculate a meaningful recursive formula for it.
openaire +1 more source

A converse to a theorem of Gauss on Gauss sums