两个平方和和tau函数：拉马努金轨迹

IF 0.9 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae Pub Date : 2025-09-06 DOI:10.1016/j.exmath.2025.125721

Bruce C. Berndt , Pieter Moree

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引用次数: 0

摘要

拉马努金，在他给哈代的著名的第一封信中，声称对可以写成两个平方和的整数的数量有一个非常精确的估计。远不为人所知的是，他还对某些素数的拉马努金τ函数的不可整除性提出了类似性质的进一步主张。在本文中，我们将提供更多的历史细节，并讨论相关的后期发展。这些照片表明，拉马努金像往常一样，是迷人荒野中的探险家，身后留下了一条迷人的小径。

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Sums of two squares and the tau-function: Ramanujan’s trail

Ramanujan, in his famous first letter to Hardy, claimed a very precise estimate for the number of integers that can be written as a sum of two squares. Far less well-known is that he also made further claims of a similar nature for the non-divisibility of the Ramanujan tau-function for certain primes. In this survey, we provide more historical details and also discuss related later developments. These show that, as so often, Ramanujan was an explorer in a fascinating wilderness, leaving behind him a beckoning trail.

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来源期刊

Expositiones Mathematicae 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

40 days

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