Published in:Journal de Théorie des Nombres de Bordeaux
Language:
English
ISSN:
1246-7405;
2118-8572
Origination:
Footnote:
Description:
<label>Abstract.</label>
<p>Let<italic>K</italic>be a number field,<italic>A</italic>be its ring of integers and<italic>p</italic>be a prime number. In this paper, we define a function<italic>μK(p)</italic>which counts the number of<italic>θ̄ ∈ A/pA</italic>such that the index of<italic>θ</italic>is divisible by<italic>p</italic>. We give as well an explicit formula for it. Moreover, we show that the value of<italic>μK(p)</italic>determines in some cases the splitting type of<italic>p</italic>in<italic>K</italic>.</p>