Sequences and special functions in number theory and combinatorics

数论和组合学中的序列和特殊函数

• 批准号: 9328-2012
• 负责人: Dilcher, Karl
• 金额: $ 1.82万
• 依托单位: Dalhousie University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=568661
• 关键词: Sequences; special; functions; number; theory

Much of the proposed research can be described as "classical", dealing with mathematical objects that have interested mathematicians for decades, in some cases even centuries. However, new methods make it worthwhile to take a fresh look at old objects, with the hope of obtaining new results. Also, advances in computer technology and in algorithms make it possible to do "mathematical experiments", sometimes at a large scale, and use the outcomes as a basis for theoretical investigations which often lead to new and sometimes unexpected results. The objects to be studied in this proposal include prime numbers and congruences, factors of special integers, polynomials, infinite series, and various special sequences of numbers and functions. The expected results contribute to a deeper understanding of the objects under investigation and have no immediate applications outside of mathematics. However, as is usually the case when one deals with large integers, prime numbers, or polynomials, there is always the possibility of applications in cryptography, the science behind data security. Although this is not the main purpose of the proposed research, I will keep such possible applications in mind.

许多提议的研究都可以描述为“古典”，它处理数学家几十年来感兴趣的数学对象，在某些情况下甚至几个世纪以来。但是，新方法值得重新看一下旧物体，并希望获得新的结果。同样，计算机技术和算法的进步使得进行“数学实验”，有时是大规模进行的，并将结果用作理论研究的基础，这通常会导致新的，有时甚至是意外的结果。 该提案中要研究的对象包括质数和一致性，特殊整数的因素，多项式，无限序列以及各种数字和功能的特殊序列。预期的结果有助于更深入地了解正在调查的对象，并且在数学之外没有立即应用。但是，正如通常处理大整数，质数或多项式的情况一样，总是有可能在加密术中应用程序，这是数据安全背后的科学。尽管这不是拟议研究的主要目的，但我将牢记这种可能的应用程序。