In this paper we deal with integrals whose integrand has a rapidly oscillating zeroorder Bessel function of the first kind with real parameters in its argument which can become large. We introduce and tabulate model integrals which depend on a single parameter, which can determine the behavior of the original integral near the zeros of the argument of the Bessel function. As an example of the u...

Two quadrature rules for the approximate evaluation of Cauchy principal value integrals, with nodes at the zeros of appropriate orthogonal polynomials, are discussed. An expression for the truncation error, in terms of higher order derivatives, is given for each rule. In addition, two theorems, containing sufficient conditions for the convergence of the sequence of quadrature rules to the integ...

The evaluation of the matrix elements of the Coulomb interaction in calculations using the Lippmann–Schwinger (or related) equations is complicated by the existence of a singularity in the integrand. One method of handling this singularity is to use a procedure commonly called the Lande subtraction. A procedure is outlined which relates the subtraction integrals to formulae involving the zeros ...

This paper gives an explicit formula for the size of the isogeny class of a Hilbert-Blumenthal abelian variety over a finite field. More precisely, let OL be the ring of integers in a totally real field dimension g over Q, let N0 and N be relatively prime square-free integers, and let k be a finite field of characteristic relatively prime to both N0N and disc(L,Q). Finally, let (X/k, ι, α) be a...

the aim of this note is to characterize the finite groups in which all non-linear irreducible characters have distinct zero entries number.

The construction of supersymmetric invariant integrals is discussed in a superspace setting. The formalism is applied to D = 4, N = 4 SYM and used to construct the F 2 , F 4 and (F 5 + ∂ 2 F 4) terms in the effective action of coincident D-branes. The results are in agreement with those obtained by other methods. A simple derivation of the abelian ∂ 4 F 4 invariant is given and generalised to t...