most citedRemarks on the disproof of the unit distance conjecture

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math.NT2025

Secondary terms in the counting functions of quartic fields

Arul Shankar, Jacob Tsimerman

We prove that the smoothed counting function of the set of quartic fields, satisfying any finite set of local conditions, can be written as a linear combination of $X,X^{5/6}\log X…

math.NT2025

Secondary terms in the counting functions of quartic fields II

Arul Shankar, Jacob Tsimerman

We determine the smoothed counts of -quartic fields with bounded discriminant, satisfying any finite specified set of local conditions, as the sum of two main terms with a pow…