Algebraic number fields with large class number
Izvestiya. Mathematics , Tome 8 (1974) no. 5, pp. 967-978
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We prove that “almost all” real quadratic fields of a given type have a large ideal class number. For example, the number of ideal classes of the fields $\mathbf Q\bigl(\sqrt{m(m+1)(m+2)(m+3)}\,\bigr)$, where $\mathbf Q$ is the field of rational numbers, grows unbounded with $m$, as $m$ ranges through all natural numbers, except for a very sparse sequence. An analogous fact is established for the fields of Ankeny–Brauer–Chowla [5].
@article{IM2_1974_8_5_a0,
author = {V. G. Sprindzhuk},
title = {Algebraic number fields with large class number},
journal = {Izvestiya. Mathematics },
pages = {967--978},
publisher = {mathdoc},
volume = {8},
number = {5},
year = {1974},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_1974_8_5_a0/}
}
V. G. Sprindzhuk. Algebraic number fields with large class number. Izvestiya. Mathematics , Tome 8 (1974) no. 5, pp. 967-978. http://geodesic.mathdoc.fr/item/IM2_1974_8_5_a0/