田野里的小班数在家庭里 $$\mathbb {Q}(\sqrt{9m^2+4m})$$

IF 0.6 3区数学 Q3 MATHEMATICS

Ramanujan Journal Pub Date : 2023-01-30 DOI:10.1007/s11139-022-00695-w

Nimish Kumar Mahapatra, Prem Prakash Pandey, Mahesh Kumar Ram

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引用次数: 1

摘要

我们研究了实数二次域$\mathbb{Q}(\sqrt{9m^2+ 4m})$的第一类问题，其中$m$是一个奇整数。我们证明，对于$m \equiv 1 \pmod 3$，只有一个类为1的字段，也只有一个类为2的字段。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Fields of small class number in the family $$\mathbb {Q}(\sqrt{9m^2+4m})$$

We study the class number one problem for real quadratic fields $\mathbb{Q}(\sqrt{9m^2+ 4m})$, where $m$ is an odd integer. We show that for $m \equiv 1 \pmod 3$ there is only one such field with class number one and only one such field with class number two.

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来源期刊

Ramanujan Journal 数学-数学

CiteScore

1.40

自引率

14.30%

发文量

133

审稿时长

6-12 weeks

期刊介绍： The Ramanujan Journal publishes original papers of the highest quality in all areas of mathematics influenced by Srinivasa Ramanujan. His remarkable discoveries have made a great impact on several branches of mathematics, revealing deep and fundamental connections. The following prioritized listing of topics of interest to the journal is not intended to be exclusive but to demonstrate the editorial policy of attracting papers which represent a broad range of interest: Hyper-geometric and basic hyper-geometric series (q-series) * Partitions, compositions and combinatory analysis * Circle method and asymptotic formulae * Mock theta functions * Elliptic and theta functions * Modular forms and automorphic functions * Special functions and definite integrals * Continued fractions * Diophantine analysis including irrationality and transcendence * Number theory * Fourier analysis with applications to number theory * Connections between Lie algebras and q-series.