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math.NT2026
Criterion set for diagonal forms of higher degree
Om Prakash
The 290-Theorem of Bhargava-Hanke completely classifies all universal quadratic forms over the rational integers in terms of a finite criterion set: a positive definite quadratic f…
math.NT2026
There are consecutive cubic fields with large class numbers, when ordered by discriminant
Vitezslav Kala, Om Prakash
We consider cubic number fields ordered by their discriminants, and show that there exist arbitrarily long sequences that contain only fields with class numbers greater than a give…