We derive uniform asymptotic expressions of some Abel sums appearing in some problems in coding theory and indicate the usefulness of these sums in other fields, like empirical processes, machine maintenance, analysis of algorithms, probabilistic number theory, queuing models, etc.

We construct an example of a series that is Abel summable but whose associated power series does not converge on angular sectors. We also give some related results.

Martin Abel* *Middlebury College, 14 Old Chapel Rd, Middlebury, VT 05753 (email: mabel{at}middlebury.edu).

Recently, Chen, Hou and Jin used both Abel’s lemma on summation by parts and Zeilberger’s algorithm to generate recurrence relations for definite summations. They also proposed the Abel-Gosper method to evaluate some indefinite sums involving harmonic numbers. In this paper, we use the Abel-Gosper method to prove an identity involving the generalized harmonic numbers. Special cases of this resu...

The Abel inversion, used to reconstruct axisymmetric radial profiles from line-of-sight intensity measurements, is increasingly used to make spatially resolved combustion measurements. An Abel deconvolution is valid only when incoming rays are parallel, whereas most practical optical setups used for emission imaging consist of single-lens and multilens systems that collect light in a cone, over...

Contents 1. Introduction 1 1.1. Notation and Conventions 2 1.2. Brill-Noether varieties and Abel maps 4 1.3. Stability and semistability 6 2. Technical groundwork 9 2.1. Basic estimates 9 2.2. Basic cases 12 2.3. Divisors imposing independent conditions 14 3. Irreducibility and dimension 19 3.1. Irreducible components of the Theta divisor 19 3.2. Dimension of the image of the Abel map 24 4. Com...