On the degree of the L -function associated with an exponential sum

Alan Adolphson; Steven Sperber

Compositio Mathematica (1988)

  • Volume: 68, Issue: 2, page 125-159
  • ISSN: 0010-437X

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Adolphson, Alan, and Sperber, Steven. "On the degree of the $L$-function associated with an exponential sum." Compositio Mathematica 68.2 (1988): 125-159. <http://eudml.org/doc/89932>.

@article{Adolphson1988,
author = {Adolphson, Alan, Sperber, Steven},
journal = {Compositio Mathematica},
keywords = {exponential sum; degree character sum; L-function; total degree; Riemann hypothesis},
language = {eng},
number = {2},
pages = {125-159},
publisher = {Kluwer Academic Publishers},
title = {On the degree of the $L$-function associated with an exponential sum},
url = {http://eudml.org/doc/89932},
volume = {68},
year = {1988},
}

TY - JOUR
AU - Adolphson, Alan
AU - Sperber, Steven
TI - On the degree of the $L$-function associated with an exponential sum
JO - Compositio Mathematica
PY - 1988
PB - Kluwer Academic Publishers
VL - 68
IS - 2
SP - 125
EP - 159
LA - eng
KW - exponential sum; degree character sum; L-function; total degree; Riemann hypothesis
UR - http://eudml.org/doc/89932
ER -

References

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  1. 1 A. Adolphson and S. Sperber; Exponential sums on the complement of a hypersurface. American Journal of Math.102 (1980) 461-487. Zbl0444.12016MR573096
  2. 2 A. Adolphson and S. Sperber; Character sums in finite fields. Comp. Math.52 (1984) 325-354. Zbl0561.12008MR756726
  3. 3 A. Adolphson: On the Dwork trace formula. Pacific Journal of Math.113 (1984) 257-268. Zbl0552.12011MR749535
  4. 4 E. Bombieri: On exponential sums in finite fields. American Journal of 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 B. Dwork: On the rationality of the zeta function of an algebraic variety. American Journal of Math.82 (1960) 631-648. Zbl0173.48501MR140494
  7. 7 B. Dwork: On the zeta function of a hypersurface. Publ. Math. I.H.E.S.12 (1962) 5-68. Zbl0173.48601MR159823
  8. 8 D. Eisenbud and E.G. Evans, Jr: Every algebraic set in n-space is the intersection of nhypersurfaces. Inventiones Math.19 (1973) 107-112. Zbl0287.14002MR327783
  9. 9 M. Fried and M. Jarden: Field Arithmetic, Springer-Verlag, Berlin, Heidelberg1986. Zbl0625.12001MR868860
  10. 10 M. Fried: L-series on a Galois Stratification, preprint. 
  11. 11 L. Illusie: Theorie de Brauer et caractéristique d'Euler-Poincaré. Astérisque82-83 (1981) 161-172. Zbl0496.14013MR629127
  12. 12 J.P. Serre: Endomorphismes completement continus des espaces de Banach p-adiques. Publ. Math. I.H.E.S.12 (1962) 69-85. Zbl0104.33601MR144186
  13. 13 S. Sperber: On the L-functions associated with certain exponential sums, Journal of Number Theory12 (1980) 141-153. Zbl0444.12015MR578806
  14. 14 U. Storch: Bemerkung zu einem Satz von M. Kneser. Arch Math.23 (1972) 403-404. Zbl0248.13006MR321921
  15. 15 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

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