The number of points on certain families of hypersurfaces over finite fields

Neal Koblitz

Compositio Mathematica (1983)

  • Volume: 48, Issue: 1, page 3-23
  • ISSN: 0010-437X

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Koblitz, Neal. "The number of points on certain families of hypersurfaces over finite fields." Compositio Mathematica 48.1 (1983): 3-23. <http://eudml.org/doc/89566>.

@article{Koblitz1983,
author = {Koblitz, Neal},
journal = {Compositio Mathematica},
keywords = {finite ground field; monomial deformations; generalized hypergeometric functions; action of group; Barne integral},
language = {eng},
number = {1},
pages = {3-23},
publisher = {Martinus Nijhoff Publishers},
title = {The number of points on certain families of hypersurfaces over finite fields},
url = {http://eudml.org/doc/89566},
volume = {48},
year = {1983},
}

TY - JOUR
AU - Koblitz, Neal
TI - The number of points on certain families of hypersurfaces over finite fields
JO - Compositio Mathematica
PY - 1983
PB - Martinus Nijhoff Publishers
VL - 48
IS - 1
SP - 3
EP - 23
LA - eng
KW - finite ground field; monomial deformations; generalized hypergeometric functions; action of group; Barne integral
UR - http://eudml.org/doc/89566
ER -

References

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  1. [1] P. Appell and J. Kampé De Fériet: Fonctions hypergéométriques et hyper-sphériques; polynomes d'Hermite. Gauthier-Villars, Paris, 1926. Zbl52.0361.13JFM51.0281.09
  2. [2] H. Davenport and H. Hasse: Die Nullstellen der Kongruenzzetafunktionen in gewissen zyklischen Fällen. J. Reine Angew. Math.172 (1935) 151-182. Zbl0010.33803JFM60.0913.01
  3. [3] J. Delsarte: Nombre de solutions des equations polynomiales sur un corps fini. Sém. Bourbaki 39-01(Mars 1951). 
  4. [4] B. Dwork: On p-adic analysis. Proc. Annual Sci. Conf., Belfer Grad. School Sci., Yeshiva Univ., New York, 1965-66, pp 129-154. MR261068
  5. [5] A. Erdélyi: Integraldarstellungen hypergeometrischer Funktionen. Quar. J. Math.8 (1937) 267-277. Zbl0018.01903JFM63.0320.03
  6. [6] E. Furtado Gomida: On the theorem of Artin-Weil. Bol. Soc. Mat. São Paulo4 (1949, 1951) 1-18. MR62174
  7. [7] K. Ireland and M. Rosen: Elements of number theory including an introduction to equations over finite fields. Bogden & Quigley Inc., Tarrytown-on-Hudson, N.Y., 1972. Zbl0248.10002MR554185
  8. [8] N. Katz: Algebraic solutions of differential equations (p-curvature and the Hodge filtration). Inventiones Math.18 (1972) 1-118. Zbl0278.14004MR337959
  9. [9] N. Koblitz: p-adic analysis: a short course on recent work. Cambridge Univ. Press, 1980. Zbl0439.12011MR591682
  10. [10] E. Rainville: Special functions. Macmillan, New York, 1960. Zbl0092.06503MR107725
  11. [11] A. Weil: Numbers of solutions of equations in finite fields. Bull. A.M.S.55 (1949) 497-508. Zbl0032.39402MR29393
  12. [12] G.N. Watson and E.T. Whittaker: A course of modern analysis, 4th ed. Cambridge Univ. Press, Cambridge, 1927. Zbl45.0433.02MR1424469JFM45.0433.02

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