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arXiv · 1710.09760

Pell-type equations and class number of the maximal real subfield of a cyclotomic field

Azizul Hoque·Kalyan Chakraborty
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Abstract

We investigate the solvability of the Diophantine equation $x^2-my^2=\pm p$ in integers for certain integer $m$ and prime $p$. Then we apply these results to produce family of maximal real subfield of a cyclotomic field whose class number is strictly bigger than $1$.

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Azizul Hoque, Kalyan Chakraborty. 2017-10-26. Pell-type equations and class number of the maximal real subfield of a cyclotomic field. https://arxiv.org/abs/1710.09760

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