拉马努金猜想及其应用

Wen-Ching Winnie Li
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引用次数: 6

摘要

在本文中,我们回顾了经典和现代背景下的拉马努金猜想,并解释了它在计算机科学中的各种应用,包括光谱极值组合对象的显式构造,称为拉马努金图和拉马努金复合体,均匀分布在球体上的点,以及量子计算中的金门集。讨论了Ramanujan图/复形与满足黎曼假设的zeta函数之间的联系。这篇文章是“Srinivasa Ramanujan:庆祝他当选财政部长一百周年”讨论会议的一部分。
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The Ramanujan conjecture and its applications
In this paper, we review the Ramanujan conjecture in classical and modern settings and explain its various applications in computer science, including the explicit constructions of the spectrally extremal combinatorial objects, called Ramanujan graphs and Ramanujan complexes, points uniformly distributed on spheres, and Golden-Gate Sets in quantum computing. The connection between Ramanujan graphs/complexes and their zeta functions satisfying the Riemann hypothesis is also discussed. This article is part of a discussion meeting issue ‘Srinivasa Ramanujan: in celebration of the centenary of his election as FRS’.
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