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On the Schertz Conjecture

Part of: Arithmetic algebraic geometry Algebraic number theory: global fields

Published online by Cambridge University Press:  08 February 2019

Ja Kyung Koo  and
Dong Sung Yoon
Ja Kyung Koo
Affiliation:
Department of Mathematical Sciences, KAIST, Daejeon 34141, Republic of Korea (jkkoo@math.kaist.ac.kr)
Dong Sung Yoon
Affiliation:
Department of Mathematics Education, Pusan National University, Busan 46241, Republic of Korea (dsyoon@pusan.ac.kr)
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Abstract

Schertz conjectured that every finite abelian extension of imaginary quadratic fields can be generated by the norm of the Siegel–Ramachandra invariants. We present a conditional proof of his conjecture by means of the characters on class groups and the second Kronecker limit formula.

Keywords

class field theorymodular units

MSC classification

Primary: 11R37: Class field theory
Secondary: 11G16: Elliptic and modular units
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 3 , August 2019 , pp. 837 - 845
Copyright
Copyright © Edinburgh Mathematical Society 2019 

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References

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