Suppression of Dielectronic Recombination Due to Finite Density Effects. II. Analytical Refinement and Application to Density-dependent Ionization Balances and AGN Broad-line Emission
- Award ID(s):
- 1816537
- PAR ID:
- 10100101
- Date Published:
- Journal Name:
- The Astrophysical Journal Supplement Series
- Volume:
- 237
- Issue:
- 2
- ISSN:
- 1538-4365
- Page Range / eLocation ID:
- 41
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract LetL/Kbe a Galois extension of number fields with Galois groupG. We show that if the density of prime ideals inKthat split totally inLtends to 1/∣G∣ with a power saving error term, then the density of prime ideals inKwhose Frobenius is a given conjugacy classC⊂Gtends to ∣C∣/∣G∣ with the same power saving error term. We deduce this by relating the poles of the corresponding Dirichlet series to the zeros ofζL(s)/ζK(s).more » « less
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