L-Functions

99780392研究者和他的合作者提议研究解析数论中的一些问题。 具体来说，他们试图证明一个渐近公式的大筛不等式，这将有应用程序之间的小差距零点的狄利克雷L-函数和平均值公式的第六和第八时刻狄利克雷L-函数。 此外，他们想证明有无穷多个狄利克雷L-函数与没有正真实的零点的真实的原始特征标相关联。 这个断言不适用于任何无限族的L-函数。 此外，他们将研究黎曼假设的Balazard-Saias准则。 例如，这个标准是否等价于黎曼假设？数论是数学的一个分支，研究涉及整数的问题。 数论在编码、网络、数据压缩和密码学中的应用将数论推向了现代数学的前沿。L-函数为研究数论中的许多问题提供了重要的工具，然而我们对L-函数的基本性质的理解是不完整的。 研究者和他的合作者试图填补我们对L-函数的基本知识中的一些空白。

99780392The investigator and his collaborators propose to study some problems in analytic number theory. Specifically, they seek to prove an asymptotic formula for the large sieve inequality; this would have applications to small gaps between zeros of Dirichlet L-functions and to mean value formulae for sixth and eighth moments of Dirichlet L-functions. Further, they want to show that there are infinitely many Dirichlet L-functions associated with real primitive characters that have no positive real zeros. This assertion is not known to hold for any infinite family of L-functions. Also, they will investigate the Balazard-Saias criterion for the Riemann Hypothesis. For example, is this criterion equivalent to the Riemann Hypothesis? Number theory is a branch of mathematics that deals with problems involving whole numbers. Applications of number theory to coding, networking, data compression, and cryptography have thrust number theory into the forefront of modern mathematics. L-functions provide an important tool for investigating many questions of number theory, yet our understanding of the fundamental properties of L-functions is incomplete. The investigator and his collaborators seek to fill in some of the gaps in our basic knowledge of L-functions.