# MODULAR CURVES AND THE CLASS NUMBER ONE PROBLEM

@inproceedings{Booher2014MODULARCA, title={MODULAR CURVES AND THE CLASS NUMBER ONE PROBLEM}, author={Jeremy Booher}, year={2014} }

There are several approaches. Heegner [9] gave a proof in 1952 using the theory of modular functions and complex multiplication. It was dismissed since there were gaps in Heegner’s paper and the work of Weber [18] on which it was based. In 1967 Stark gave a correct proof [16], and then noticed that Heegner’s proof was essentially correct and in fact equivalent to his own. Also in 1967, Baker gave a proof using lower bounds for linear forms in logarithms [1]. Later, Serre [14] gave a new…

## 2 Citations

Imaginary quadratic fields with class number 1

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We give an exposition of Heegner’s and Siegel’s proofs that there are exactly 9 imaginary quadratic fields with class number equal to 1. In particular, we discuss Weber’s original method of…

Quadratic points on non-split Cartan modular curves

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In this paper, we study quadratic points on the non-split Cartan modular curves [Formula: see text], for [Formula: see text] and [Formula: see text]. Recently, Siksek proved that all quadratic points…

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