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Research Article

On the zeros and singularities of p−adic trace functions

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Pages 967-978 | Received 19 Feb 2020, Accepted 15 Sep 2020, Published online: 01 Oct 2020

References

  • Achimescu, S., Alexandru, V., Popescu, N., Vâjâitu, M., Zaharescu, A. (2007). The behavior of rigid analytic functions around orbits of elements of Cp. Rend. Sem. Mat. Univ. Padova. 118:197–216.
  • Alexandru, V., Popescu, N., Vâjâitu, M., Zaharescu, A. (2013). On the zeros of Krasner analytic functions. Algebr. Represent. Theory 16(3):895–904. DOI: 10.1007/s10468-012-9338-2.
  • Alexandru, V., Popescu, N., Zaharescu, A. (1998). On the closed subfields of Cp. J. Number Theory 68(2):131–150.
  • Alexandru, V., Popescu, N., Zaharescu, A. (2001). Trace on Cp. J. Number Theory 88(1):13–48.
  • Alexandru, V., Niţu, C. C., Vâjâitu, M., Zaharescu, A. (2015). On the norm of Krasner analytic functions with applications to transcendence results. J. Pure Appl. Algebra 219(10):4607–4618. DOI: 10.1016/j.jpaa.2015.02.033.
  • Alexandru, V., Vâjâitu, M., Zaharescu, A. (2016). On p-adic analytic continuation with applications to generating elements. Proc. Edinburgh Math. Soc. 59(1):1–10. DOI: 10.1017/S0013091514000376.
  • Amice, Y. (1975). Les nombres p-adiques (Collection Sup: “Le Mathématicien”, 14). Paris: Presses Universitaires de France.
  • Artin, E. (1967). Algebraic Numbers and Algebraic Functions. New York: Gordon and Breach Science Publishers.
  • Ax, J. (1970). Zeros of polynomials over local fields—The Galois action. J. Algebra 15(3):417–428. DOI: 10.1016/0021-8693(70)90069-4.
  • Borevich, Z.I., Shafarevich, I.R. (1966). Number Theory. Pure and Applied Mathematics, Vol. 20. New York, London: Academic Press.
  • Escassut, A. (1995). Analytic Elements in p-Adic Analysis. Singapore: World Scientific Publishing.
  • Fein, B., Schacher, M. (1996). Properties of iterates and composites of polynomials. J. London Math. Soc. 54(3):489–497. DOI: 10.1112/jlms/54.3.489.
  • Fresnel, J., van der Put, M. (2004). Rigid Analytic Geometry and Its Applications. Boston, MA: Birkhauser.
  • Koblitz, N. (1980). p-Adic Analysis: A Short Course on Recent Work. London Mathematical Society Lecture Note Series, 46. Cambridge, New York: Cambridge University Press.
  • Koblitz, N. (1984). p-Adic Numbers, p-Adic Analysis, and Zeta-Functions. New York: Springer-Verlag.
  • Krasner, M. (1974). Rapport sur le prolongement analytique dans les corps valués complets par la méthode des éléments analytiques quasi-connexes. Bull. Soc. Math. Fr. Mém. 39–40:131–254. DOI: 10.24033/msmf.166.
  • Lipshitz, L. (1988). Isolated points on fibres of affinoid varieties. J. Reine Angew Math. 384:208–220.
  • Mazur, B., Swinnerton-Dyer, P. (1974). Arithmetic of Weil curves. Invent. Math. 25(1):1–61. DOI: 10.1007/BF01389997.
  • Popescu, A., Popescu, N., Vâjâitu, M., Zaharescu, A. (2002). Chains of metric invariants over a local field. Acta Arith. 103(1):27–40. DOI: 10.4064/aa103-1-4.
  • Popescu, N., Vâjâitu, M., Zaharescu, A. (2006). On the existence of trace for elements of Cp. Algebr. Represent. Theory 9(1):47–66.
  • Popescu, N., Zaharescu, A. (1995). On the structure of irreducible polynomials over local fields. J. Number Theory 52(1):98–118. DOI: 10.1006/jnth.1995.1058.
  • Popescu, N., Zaharescu, A. (1997). On the main invariant of an element over a local field. Port. Math. 54:73–83.
  • Robert, A.M. (2000). A Course in p-Adic Analysis. New York: Springer-Verlag.
  • Vâjâitu, M. (2013). Integral representations and the behavior of Krasner analytic functions around singular points. Algebr. Represent. Theory 16(6):1611–1620. DOI: 10.1007/s10468-012-9374-y.
  • Vâjâitu, M., Zaharescu, A. (2006). Trace functions and Galois invariant p-adic measures. Publ. Mat. 50:43–55. DOI: 10.5565/PUBLMAT_50106_02.

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