On Hasse's Unit Index
Djordjo Z. Milovic

TL;DR
This paper investigates the distribution of Hasse's unit index in certain CM-fields, revealing that the count of fields with a specific index grows proportionally to X divided by the square root of log X.
Contribution
It provides a new asymptotic formula for the distribution of Hasse's unit index in CM-fields of the form Q(√d, √-1).
Findings
Number of d ≤ X with Q(L)=2 is proportional to X/√(log X).
Distribution pattern of Hasse's unit index in these fields is characterized.
Asymptotic behavior of the index distribution is established.
Abstract
We study the distribution of Hasse's unit index for the CM-fields as varies among positive squarefree integers. We prove that the number of such that is proportional to .
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Taxonomy
TopicsAnalytic Number Theory Research · Advanced Algebra and Geometry · Algebraic Geometry and Number Theory
