Skip to main content

Tipp

Weitere Kapitel dieses Buchs durch Wischen aufrufen

2016 | OriginalPaper | Buchkapitel

Transfer Principles for Bounds of Motivic Exponential Functions

verfasst von : Raf Cluckers, Julia Gordon, Immanuel Halupczok

Erschienen in: Families of Automorphic Forms and the Trace Formula

Verlag: Springer International Publishing

Abstract

We study transfer principles for upper bounds of motivic exponential functions and for linear combinations of such functions, directly generalizing the transfer principles from Cluckers and Loeser (Ann Math 171:1011–1065, 2010) and Shin and Templier (Invent Math, 2015, Appendix B). These functions come from rather general oscillatory integrals on local fields, and can be used to describe, e.g., Fourier transforms of orbital integrals. One of our techniques consists in reducing to simpler functions where the oscillation only comes from the residue field.

Sie möchten Zugang zu diesem Inhalt erhalten? Dann informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt 90 Tage mit der neuen Mini-Lizenz testen!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe



 


Jetzt 90 Tage mit der neuen Mini-Lizenz testen!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt 90 Tage mit der neuen Mini-Lizenz testen!

Literatur
[CGH]
Zurück zum Zitat R. Cluckers, J. Gordon, I. Halupczok, Integrability of oscillatory functions on local fields: transfer principles. Duke Math. J. 163 (8), 1549–1600 (2014) MathSciNetCrossRefMATH R. Cluckers, J. Gordon, I. Halupczok, Integrability of oscillatory functions on local fields: transfer principles. Duke Math. J. 163 (8), 1549–1600 (2014) MathSciNetCrossRefMATH
[CGH2]
Zurück zum Zitat R. Cluckers, J. Gordon, I. Halupczok, Local integrability results in harmonic analysis on reductive groups in large positive characteristic. Ann. Sci. École Norm. Sup. (4) 47 (6), 1163–1195 (2014) R. Cluckers, J. Gordon, I. Halupczok, Local integrability results in harmonic analysis on reductive groups in large positive characteristic. Ann. Sci. École Norm. Sup. (4) 47 (6), 1163–1195 (2014)
[CGH3]
Zurück zum Zitat R. Cluckers, J. Gordon, I. Halupczok, Motivic functions, integrability, and uniform in p bounds for orbital integrals. Electron. Res. Announc. Math. 21, 137–152 (2014) MathSciNet R. Cluckers, J. Gordon, I. Halupczok, Motivic functions, integrability, and uniform in p bounds for orbital integrals. Electron. Res. Announc. Math. 21, 137–152 (2014) MathSciNet
[CGH5]
Zurück zum Zitat R. Cluckers, J. Gordon, I. Halupczok, Uniform Analysis on Local Fields and Applications to Orbital Integrals (2016) R. Cluckers, J. Gordon, I. Halupczok, Uniform Analysis on Local Fields and Applications to Orbital Integrals (2016)
[CHa]
Zurück zum Zitat R. Cluckers, I. Halupczok, Integration, uniform in all fields of p-adic numbers (2015), preprint available at arXiv:1510.08250 R. Cluckers, I. Halupczok, Integration, uniform in all fields of p-adic numbers (2015), preprint available at arXiv:1510.08250
[CHL]
Zurück zum Zitat R. Cluckers, T. Hales, F. Loeser, Transfer principle for the fundamental lemma, in Stabilisation de la formule des traces, variétés de Shimura, et applications arithmétiques, vol. I, ed. by L. Clozel, M. Harris, J.-P. Labesse, B.-C. Ngô (International Press, Boston, 2011) R. Cluckers, T. Hales, F. Loeser, Transfer principle for the fundamental lemma, in Stabilisation de la formule des traces, variétés de Shimura, et applications arithmétiques, vol. I, ed. by L. Clozel, M. Harris, J.-P. Labesse, B.-C. Ngô (International Press, Boston, 2011)
[CLb]
Zurück zum Zitat R. Cluckers, F. Loeser, Motivic integration in all residue field characteristics for Henselian discretely valued fields of characteristic zero. J. Reine Angew. Math. 701, 1–31 (2015) MathSciNetMATH R. Cluckers, F. Loeser, Motivic integration in all residue field characteristics for Henselian discretely valued fields of characteristic zero. J. Reine Angew. Math. 701, 1–31 (2015) MathSciNetMATH
[CLe]
Zurück zum Zitat R. Cluckers, F. Loeser, Constructible exponential functions, motivic Fourier transform and transfer principle. Ann. Math. 171, 1011–1065 (2010) MathSciNetCrossRefMATH R. Cluckers, F. Loeser, Constructible exponential functions, motivic Fourier transform and transfer principle. Ann. Math. 171, 1011–1065 (2010) MathSciNetCrossRefMATH
[CLo]
[Den1]
Zurück zum Zitat J. Denef, Arithmetic and Geometric Applications of Quantifier Elimination for Valued Fields. MSRI Publications, vol. 39 (Cambridge University Press, Cambridge, 2000), pp. 173–198 J. Denef, Arithmetic and Geometric Applications of Quantifier Elimination for Valued Fields. MSRI Publications, vol. 39 (Cambridge University Press, Cambridge, 2000), pp. 173–198
[Den2]
Zurück zum Zitat J. Denef, p-adic semialgebraic sets and cell decomposition. J. Reine Angew. Math. 369, 154–166 (1986) J. Denef, p-adic semialgebraic sets and cell decomposition. J. Reine Angew. Math. 369, 154–166 (1986)
[GoHa]
Zurück zum Zitat J. Gordon, T. Hales, Endoscopic transfer of orbital integrals in large residual characteristic. Am. J. Math. 138 (1) (2016) J. Gordon, T. Hales, Endoscopic transfer of orbital integrals in large residual characteristic. Am. J. Math. 138 (1) (2016)
[Pas]
Zurück zum Zitat J. Pas, Uniform p-adic cell decomposition and local zeta functions. J. Reine Angew. Math. 399, 137–172 (1989) MathSciNetMATH J. Pas, Uniform p-adic cell decomposition and local zeta functions. J. Reine Angew. Math. 399, 137–172 (1989) MathSciNetMATH
[ShTe]
Zurück zum Zitat S.-W. Shin, N. Templier, Sato-Tate theorem for families and low-lying zeros of automorphic l-functions, with Appendix A by R. Kottwitz and Appendix B by R. Cluckers, J. Gordon and I. Halupczok. Invent. Math. (2015). doi: 10.1007/s00222-015-0583-y S.-W. Shin, N. Templier, Sato-Tate theorem for families and low-lying zeros of automorphic l-functions, with Appendix A by R. Kottwitz and Appendix B by R. Cluckers, J. Gordon and I. Halupczok. Invent. Math. (2015). doi: 10.1007/s00222-015-0583-y
[YGo]
Zurück zum Zitat Z. Yun, The fundamental lemma of Jacquet and Rallis. Duke Math. J. 156 (2), 167–227 (2011). Appendix by J. Gordon Z. Yun, The fundamental lemma of Jacquet and Rallis. Duke Math. J. 156 (2), 167–227 (2011). Appendix by J. Gordon
Metadaten
Titel
Transfer Principles for Bounds of Motivic Exponential Functions
verfasst von
Raf Cluckers
Julia Gordon
Immanuel Halupczok
Copyright-Jahr
2016
DOI
https://doi.org/10.1007/978-3-319-41424-9_3

Premium Partner