Geodesic
An improvement on Schmidt’s bound on the number of number fields of bounded discriminant and small degree
Forum of Mathematics, Sigma, Tome 10 (2022)

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We prove an improvement on Schmidt’s upper bound on the number of number fields of degree n and absolute discriminant less than X for $6\leq n\leq 94$. We carry this out by improving and applying a uniform bound on the number of monic integer polynomials, having bounded height and discriminant divisible by a large square, that we proved in a previous work [7]. 
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     title = {An improvement on {Schmidt{\textquoteright}s} bound on the number of number fields of bounded discriminant and small degree},
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Manjul Bhargava; Arul Shankar; Xiaoheng Wang. An improvement on Schmidt’s bound on the number of number fields of bounded discriminant and small degree. Forum of Mathematics, Sigma, Tome 10 (2022). doi: 10.1017/fms.2022.71

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