Grant: Research Tools and Instruments - Category 1 (<$150,000)

The advances of modern computers has enabled number theorists to conjecture and discover many surprising properties of integers by computational experiments. Over the past years computers and specialized number theoretical software such as PARI and MAGMA have become an indispensable tool for many number theorists. Currently there are several ongoing computational projects under investigation by the number theory group at the University of Lethbridge. These projects include, biases in the size of arithmetic functions and moments of L-functions, congruences between modular forms, and explicit estimates for some functions of prime numbers. Our request is to purchase a high performance computer to help us in the computational parts of the above projects and in support of the research of our number theory group over the next five years. We have chosen the LINUX operating system since most of the applications and libraries that are used in number theory are designed for this environment. We are also requesting MAGMA, since this package has many of the algorithms necessary for our projects. As many of the above problems can be parallelized, multiple processors will allow the computations to be done more efficiently. Furthermore, multiple processors will allow our students to experiment with some of the new parallel algorithms that are proposed for some of these problems. The requested hardware and software will be used by the number theory group at the University of Lethbridge, our students, and our postdoctoral fellows.