Computational Problems in Number Theory

现代计算机的进步使数学家能够通过计算实验来猜测和发现整数的许多令人惊讶的性质。在过去的几年里，计算机和专门的数论软件，如PARI和MAGMA，已经成为许多数学家不可或缺的工具。目前，莱斯布里奇大学的数论小组正在调查几个正在进行的计算项目。这些问题包括：算术函数的大小偏差、L函数的矩、模形式之间的同余以及某些素数函数的显式估计。

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.