Character sums in finite fields

A. Adolphson; Steven Sperber

Compositio Mathematica (1984)

  • Volume: 52, Issue: 3, page 325-354
  • ISSN: 0010-437X

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Adolphson, A., and Sperber, Steven. "Character sums in finite fields." Compositio Mathematica 52.3 (1984): 325-354. <http://eudml.org/doc/89668>.

@article{Adolphson1984,
author = {Adolphson, A., Sperber, Steven},
journal = {Compositio Mathematica},
keywords = {Dwork-Reich trace formula; character sums; L-series; Fredholm determinant; Newton-polygon},
language = {eng},
number = {3},
pages = {325-354},
publisher = {Martinus Nijhoff Publishers},
title = {Character sums in finite fields},
url = {http://eudml.org/doc/89668},
volume = {52},
year = {1984},
}

TY - JOUR
AU - Adolphson, A.
AU - Sperber, Steven
TI - Character sums in finite fields
JO - Compositio Mathematica
PY - 1984
PB - Martinus Nijhoff Publishers
VL - 52
IS - 3
SP - 325
EP - 354
LA - eng
KW - Dwork-Reich trace formula; character sums; L-series; Fredholm determinant; Newton-polygon
UR - http://eudml.org/doc/89668
ER -

References

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  1. [1] A. Adolphson: An index theorem for p-adic differential operators. Trans. Amer. Math. Soc.216 (1976) 279-293. Zbl0297.47039MR387284
  2. [2] A. Adolphson: Appendix to: B. Dwork, Lectures on p-adic differential equations, Grundlehren der mathematischen Wissenschaften253. New York, Heidelberg, Berlin: Springer-Verlag (1982). Zbl0502.12021MR678093
  3. [3] A. Adolphson and S. Sperber: Exponential sums on the complement of a hypersurface. Amer. J. Math.102 (1980) 461-487. Zbl0444.12016MR573096
  4. [4] E. Bombieri: On exponential sums in finite fields. Amer. J. Math.88 (1966) 71-105. Zbl0171.41504MR200267
  5. [5] E. Bombieri: On exponential sums in finite fields, II. Inventiones Math.47 (1978) 29-39. Zbl0396.14001MR506272
  6. [6] H. Davenport: On character sums in finite fields. Acta Math.71 (1939) 99-121. Zbl0021.20202MR252JFM65.0116.03
  7. [7] P. Deligne and N. Katz: Groupes de Monodromie en Géométrie Algébrique, Lecture Notes in Math. No. 340. Berlin, Heidelberg, New York: Springer-Verlag (1973). Zbl0258.00005MR354657
  8. [8] B. Dwork: On the rationality of the zeta function of an algebraic variety. Amer. J. Math.82 (1960) 631-648. Zbl0173.48501MR140494
  9. [9] B. Dwork: On the zeta function of a hypersurface. Publ. Math. I.H.E.S.12 (1962) 5-68. Zbl0173.48601MR159823
  10. [10] B. Dwork: On the zeta function of a hypersurface, II. Ann. Math.80 (1964) 227-299. Zbl0173.48601MR188215
  11. [10] (a) B. Dwork: Lectures on p-adic differential equations, Grundlehren der Mathematischen Wissenschaften253. New York, Heidelberg, Berlin: Springer-Verlag (1982). Zbl0502.12021MR678093
  12. [11] H. Hasse: Theorie der relativ-zyklischen algebraischen Funktionenkörper, inbesondere bei endlichem Konstantenkörper. J. Reine u. Angew. math.172 (1934) 37-54. Zbl0010.00501JFM60.0097.01
  13. [12] L. Illusie: Théorie de Brauer et caractéristique d'Euler-Poincaré. Astérisque82 -83 (1981) 161-172. Zbl0496.14013MR629127
  14. [13] D. Reich: A p-adic fixed point formula. Amer. J. Math.91 (1969) 835-850. Zbl0213.47502MR255549
  15. [14] J-P. Serre: Endomorphismes completement continus des espaces de Banach p-adiques. Publ. Math. I.H.E.S.12 (1962) 69-85. Zbl0104.33601MR144186

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