On the behavior of Igusa,'s local zeta function in towers of field extension

Ben Lichtin

Groupe de travail d'analyse ultramétrique (1984-1985)

  • Volume: 12, Issue: 2, page 1-10

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Lichtin, Ben. "On the behavior of Igusa,'s local zeta function in towers of field extension." Groupe de travail d'analyse ultramétrique 12.2 (1984-1985): 1-10. <http://eudml.org/doc/91947>.

@article{Lichtin1984-1985,
author = {Lichtin, Ben},
journal = {Groupe de travail d'analyse ultramétrique},
keywords = {non-archimedean valued ground field; zeta function; poles; Hironaka resolution; monodromy action; unramified extension},
language = {eng},
number = {2},
pages = {1-10},
publisher = {Secrétariat mathématique},
title = {On the behavior of Igusa,'s local zeta function in towers of field extension},
url = {http://eudml.org/doc/91947},
volume = {12},
year = {1984-1985},
}

TY - JOUR
AU - Lichtin, Ben
TI - On the behavior of Igusa,'s local zeta function in towers of field extension
JO - Groupe de travail d'analyse ultramétrique
PY - 1984-1985
PB - Secrétariat mathématique
VL - 12
IS - 2
SP - 1
EP - 10
LA - eng
KW - non-archimedean valued ground field; zeta function; poles; Hironaka resolution; monodromy action; unramified extension
UR - http://eudml.org/doc/91947
ER -

References

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  1. [1] Atiyah, M., "Resolution of Singularities and Divisions of Distributions", Communication Pure & Applied Math.23 (1970), p.145-150. Zbl0188.19405MR256156
  2. [2] Bernstein, J.N. & Gel'fand, S., "Meromorophic Property of the functions Pλ," Functional Analysis & Applications, 6 (1972), p.68-69. Zbl0208.15201
  3. [3] Deligne, P., "Le formalisme du cycles evanescente" SGA7, exp. 13, SpringerLecture Notes, vol. 340. Zbl0266.14008
  4. [4] Dwork, B., "On the Rationality of the Zeta function of an algebraic variety", American J. of Math.82 (1960), p.631-648. Zbl0173.48501MR140494
  5. [5] Denef, J., "Rationality of the Poincare Series associated to the p-adic points on a variety", Inv. Math.77 (1984), p.1-23. Zbl0537.12011MR751129
  6. [6] Denef, J., "Poles of Complex Powers and Newton Polyhedra" (preprint). Zbl0854.11066
  7. [7] Gel'fand, I. & Shilov, G., Les Distributions, Dunod, Paris (1972). 
  8. [8] Igusa, J.I., "Complex Powers and Asymptotic Expansions", J. Reine Angew. Math.268/269, p.110-130 (1974). ibid278/279, p.307-321 (1975). Zbl0287.43007
  9. [9] Igusa, J.I., "Complex Powers of Irreducible Algebroid Curves " (preprint) Zbl0605.14029MR895155
  10. [10] Lichtin, B., "Upper semi-continuity Properties of Poles of |f|s" (to appear in Japan-U.S. Conf. on Complex Singularities 1984). Zbl0615.32007
  11. [11] Lichtin, B. & Meuser, D., "Poles of a Local Zeta Function and Newton Polygons" (to appear in Compositio Math.). Zbl0606.14022MR799820
  12. [12] Meuser, D., "On the poles of a local zeta function for curves", Inv. Math.73 (1983), p.445-465. Zbl0503.14009MR718941
  13. [13] Meuser, D., "Meromorphic Continuation of a Zeta Function of Weil and Igusa Type" (to appear in Inv. Math.) Zbl0571.12009MR848683

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