Om Prakash

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20242026

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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…

math.NT2024

Northcott property and universality of higher degree forms

Om Prakash

Let $K$ be a totally real number field, $d$ a positive integer, and $Q$ a higher degree form over $K$ . We prove that there are at most finitely many totally real extensions $L / K$ o…

math.NT2024

There is no 290-Theorem for higher degree forms

Vitezslav Kala, Om Prakash

We study the universality of forms of degrees greater than 2 over rings of integers of totally real number fields. We show that such universal forms always exist, but cannot be cha…