Coleman’s theory of p-adic integration figures prominently in several number-theoretic applications, such as finding torsion and rational points on curves, and computing p-adic regulators in K-theory (including p-adic heights on elliptic curves). We describe an algorithm for computing Coleman integrals on hyperelliptic curves, and its implementation in Sage.

We present a method for computing a posteriori error bounds for piecewise linear approximate solutions of elliptic equations of monotone type. The method is based on a relation between a line integral on an edge of a triangle and volume integrals in the triangle.

We describe an analytic method for the computation of equilibrium shapes for two-dimensional vesicles characterized by a Helfrich elastic energy. We derive boundary value problems and solve them analytically in terms of elliptic functions and elliptic integrals. We derive solutions by prescribing length and area, or displacements and angle boundary conditions. The solutions are compared to solu...

Abstract. Using multiple q-integrals and a determinant evaluation, we establish a multivariable extension of Bailey’s nonterminating 10φ9 transformation. From this result, we deduce new multivariable terminating 10φ9 transformations, 8φ7 summations and other identities. We also use similar methods to derive new multivariable 1ψ1 and 6ψ6 summations. Some of our results are extended to the case o...

We compute the critical L-values of some weight 3, 4, or 5 modular forms, by transforming them into integrals of the complete elliptic integral K. In doing so, we prove closed form formulas for some moments of K ′3. Many of our L-values can be expressed in terms of Gamma functions, and this also gives new lattice sum evaluations.

A new class of integrable Newton systems in Rn is presented. They are characterized by the existence of two quadratic integrals of motion of so-called cofactor type, and are therefore called cofactor pair systems. This class includes as special cases conservative systems separable in elliptic or parabolic coordinates, as well as many Newton systems previously derived as reductions of soliton hi...

This is a survey and expository article. Some new developments on refinements, generalizations, applications of Jordan’s inequality and related problems, including some results about Wilker-Anglesio’s inequality, some estimates for three kinds of complete elliptic integrals and several inequalities for the remainder of power series expansion of ex, are summarized.

The present study is a continuation of a previous one on ”hyperelliptic” axisymmetric equilibria started in [Tasso and Throumoulopoulos, Phys. Plasmas 5, 2378 (1998)]. Specifically, some equilibria with incompressible flow nonaligned with the magnetic field and restricted by appropriate side conditions like ”isothermal” magnetic surfaces, ”isodynamicity” or P +B/2 constant on magnetic surfaces ...

A bstract We studied the two-loop non-factorizable Feynman diagrams for t -channel single-top production process in quantum chromodynamics. present a systematic computation of master integrals with one internal massive propagator which complete uniform transcendental basis can be built. The are derived by means canonical differential equations and integrals. results expressed form Goncharov pol...

We calculate explicitly in terms of complete elliptic integrals the metric on the moduli space of tetrahedrally-symmetric, charge four, SU(2) monopoles. Using this we verify that in the asymptotic regime the metric of Gibbons and Manton is exact up to exponentially suppressed corrections. ∗This work was supported in part by the Nuffield Foundation