Mathematical Sciences: Finite Difference Techniques and Irreducibility Theorems in Analytic Number Theory

这个奖项资助了迈克尔·菲拉塞塔教授的继续工作，因为他完善了他与奥格尼安·特里方诺夫教授共同开发的新的微分技术。菲拉塞塔教授有几个具体的问题，他将应用该方法。这些问题包括关于模1的相当一般的函数的整数值分布的问题，以及关于无平方数之间的间隙和平方满数之间的间隙的问题。这项工作属于解析数论的一般领域。解析数论领域将微积分技术应用于整数的离散领域。微积分的发展是为了帮助分析连续的数学对象。使用连续方法研究离散物体的想法已经有两个世纪的历史了，但随着现代解析数学家的工作，该领域获得了新的新生，并导致了对整数的更深层次的理解。***

Filaseta This award funds the continued work of Professor Michael Filaseta as he refines the new differencing techniques he developed in joint work with Prof. Ognian Trifonov. Prof. Filaseta has several specific problems on which he will apply the method. These problems include questions about the distribution of integer values of fairly general functions modulo one, and questions about the gaps between squarefree numbers and gaps between squarefull numbers. This work is in the general field of analytic number theory. The field of analytic number theory applies the techniques of calculus to the discrete realm of the whole numbers. Calculus was developed to aid the analysis of continuous mathematical objects. The idea of using continuous methods to investigate discrete objects is two centuries old, but with the work of the modern analytic number theorists, the field has had a new rebirth and led to a deeper understanding of the whole numbers. ***