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On the local density formula and the Gross–Keating invariant with an Appendix ‘The local density of a binary quadratic form’ by T. Ikeda and H. Katsurada
- Source :
- Mathematische Zeitschrift. 296:1235-1269
- Publication Year :
- 2020
- Publisher :
- Springer Science and Business Media LLC, 2020.
-
Abstract
- T. Ikeda and H. Katsurada have developed the theory of the Gross-Keating invariant of a quadratic form in their recent papers [IK1] and [IK2]. In particular, they prove that the local factor of the Fourier coefficients of the Siegel-Eisenstein series is completely determined by the Gross-Keating invariant with extra datum, called the extended GK datum, in [IK2]. On the other hand, such local factor is a special case of the local densities for a pair of two quadratic forms. Thus we propose a general question if the local density can be determined by certain series of the Gross-Keating invariants and the extended GK datums. In this paper, we prove that the answer to this question is affirmative, for the local density of a single quadratic form defined over an unramified finite extension of $\mathbb{Z}_2$. In the appendix, T. Ikeda and H. Katsurada compute the local density formula of a single binary quadratic form defined over any finite extension of $\mathbb{Z}_2$.<br />32 pages
- Subjects :
- Pure mathematics
Mathematics - Number Theory
Mathematics::Number Theory
General Mathematics
010102 general mathematics
Local factor
01 natural sciences
Quadratic form
0103 physical sciences
FOS: Mathematics
11E08, 11E95, 14L15, 20G25
Binary quadratic form
Number Theory (math.NT)
010307 mathematical physics
0101 mathematics
Invariant (mathematics)
Local field
Fourier series
Mathematics
Subjects
Details
- ISSN :
- 14321823 and 00255874
- Volume :
- 296
- Database :
- OpenAIRE
- Journal :
- Mathematische Zeitschrift
- Accession number :
- edsair.doi.dedup.....4ed00bf8b619e08987a91707f5b47a6e