Computational Problems in Number Theory

数论中的计算问题

• 批准号: 421894-2012
• 负责人: Akbary, Amir
• 金额: $ 0.76万
• 依托单位: University of Lethbridge
• 依托单位国家: 加拿大
• 项目类别: Research Tools and Instruments - Category 1 (<$150,000)
• 财政年份: 2011
• 资助国家: 加拿大
• 起止时间: 2011-01-01 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=495682
• 关键词: Computational; Problems; Number; Theory

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.

现代计算机的进步使数论学家能够通过计算实验推测和发现整数的许多惊人性质。在过去的几年里，计算机和专门的数论软件，如PARI和MAGMA，已经成为许多数论学家不可或缺的工具。目前，莱斯布里奇大学数论小组正在研究几个正在进行的计算项目。这些项目包括，算术函数和l函数矩的大小偏差，模形式之间的同余，以及一些素数函数的显式估计。