Algorithms for Coleman and Vologodsky integrals, p-adic heights, and arithmetic applications

Project Details

Description

One of the oldest problems in mathematics is to find solutions to equations in integers or fractions. An example of such an equation is 3:2 + g,/2 : 22, whose solutions give the sides of right triangles. The simplest solution is at : 3, y : 4, z : 5. Fermat"s famous last theorem is also about such equations.

Coleman integrals are an important tool in number theory. Its most recent application is finding solutions to equations. For example, using techniques of Coleman integration, one of us was involved in a project for finding all solutions to the so called "’ cursed curve” equation.

Both of us were deeply involved in developing methods for the com- putation of Coleman integrals and their various applications. In recent years, Especially since it was discovered that Coleman integrals can be used for solving equations, there is a growing demand for more efficient algorithms for computations of Coleman integrals.

In this project we aim to develop improved methods for the computa- tion of Coleman integrals. The ultimate goal is to produce a computer program that will get as input a function and will find its integral. This will contribute to the large community of mathematicians involved in devising techniques for solving equations and ultimately anyone in the scientific and engineering community in need of solving equations.

StatusActive
Effective start/end date1/01/22 → …

Funding

  • United States-Israel Binational Science Foundation (BSF)

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