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math.NT2025
A class number problem for imaginary cyclic number fields of 2-power degrees
Stéphane R. Louboutin
In 2024, M. K. Ram proved that the class number of an imaginary cyclic quartic number field is never equal to a prime . Here we greatly generalize this result to…
math.NT2025
An asymptotic on the logarithms of the relative class numbers of imaginary abelian number fields of prime conductor and large degree
Stéphane Louboutin
An asymptotic on the logarithms of the relative class numbers of the cyclotomic number fields of prime conductors is known. Here we give an asymptotic on the logarithms of the…