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EULER–KRONECKER CONSTANTS FOR CYCLOTOMIC FIELDS.
- Source :
-
Bulletin of the Australian Mathematical Society . Feb2023, Vol. 107 Issue 1, p79-84. 6p. - Publication Year :
- 2023
-
Abstract
- The Euler–Mascheroni constant $\gamma =0.5772\ldots \!$ is the $K={\mathbb Q}$ example of an Euler–Kronecker constant $\gamma _K$ of a number field $K.$ In this note, we consider the size of the $\gamma _q=\gamma _{K_q}$ for cyclotomic fields $K_q:={\mathbb Q}(\zeta _q).$ Assuming the Elliott–Halberstam Conjecture (EH), we prove uniformly in Q that $$ \begin{align*} \frac{1}{Q}\sum_{Q In other words, under EH, the $\gamma _q /\!\log q$ in these ranges converge to the one point distribution at $1$. This theorem refines and extends a previous result of Ford, Luca and Moree for prime $q.$ The proof of this result is a straightforward modification of earlier work of Fouvry under the assumption of EH. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LOGICAL prediction
*CYCLOTOMIC fields
Subjects
Details
- Language :
- English
- ISSN :
- 00049727
- Volume :
- 107
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Bulletin of the Australian Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 161234431
- Full Text :
- https://doi.org/10.1017/S0004972722000521