Higher solutions of hypergeometric systems and Dwork cohomology

Alan Adolphson

Rendiconti del Seminario Matematico della Università di Padova (1999)

  • Volume: 101, page 179-190
  • ISSN: 0041-8994

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Adolphson, Alan. "Higher solutions of hypergeometric systems and Dwork cohomology." Rendiconti del Seminario Matematico della Università di Padova 101 (1999): 179-190. <http://eudml.org/doc/108483>.

@article{Adolphson1999,
author = {Adolphson, Alan},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {-modules; hypergeometric functions; monomials; hypergeometric differential module; Dwork cohomology},
language = {eng},
pages = {179-190},
publisher = {Seminario Matematico of the University of Padua},
title = {Higher solutions of hypergeometric systems and Dwork cohomology},
url = {http://eudml.org/doc/108483},
volume = {101},
year = {1999},
}

TY - JOUR
AU - Adolphson, Alan
TI - Higher solutions of hypergeometric systems and Dwork cohomology
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1999
PB - Seminario Matematico of the University of Padua
VL - 101
SP - 179
EP - 190
LA - eng
KW - -modules; hypergeometric functions; monomials; hypergeometric differential module; Dwork cohomology
UR - http://eudml.org/doc/108483
ER -

References

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  1. [1] A. Adolphson, Hypergeometric functions and rings generated by monomials, Duke Math. J., 73 (1994), pp. 269-290. Zbl0804.33013MR1262208
  2. [2] A. Adolphson - S. Sperber, Exponential sums and Newton polyhedra: cohomology and estimates, Ann. of Math., 130 (1989), pp. 367-406. Zbl0723.14017MR1014928
  3. [3] I.N. Bernstein, The analytic continuation of generalized functions with respect to a parameter, Functional Analysis and its Applications, 6 (1972), pp. 273-285 (English translation). Zbl0282.46038MR320735
  4. [4] A. Borel et al., Algebraic D-Modules, Academic Press (1987). Zbl0642.32001MR882000
  5. [5] B. Dwork, On the zeta function of a hypersurface, Publ. Math. I. H. E. S., 12 (1962), pp. 5-68. Zbl0173.48601MR159823
  6. [6] B. Dwork, On the zeta function of a hypersurface, III, Ann. of Math., 83 (1966), pp. 457-519. Zbl0173.48601MR209296
  7. [7] B. Dwork - F. LOESER, Hypergeometric series, Japanese J. Math., 19 (1993), pp. 81-129. Zbl0796.12005MR1231511
  8. [8] L. Ehrenpreis, Fourier Analysis in Several Complex Variables, John Wiley and Sons (1970). Zbl0195.10401MR285849
  9. [9] I.M. Gelfand - A.V. Zelevinskii - M.M. Kapranov, Hypergeometric functions and toral manifolds, Functional Analysis and its Applications, 23 (1989), pp. 94-106 (English translation). Zbl0721.33006MR1011353
  10. [10] M. Hochster, Rings of invariants of tori, Cohen-Macaulay rings generated by monomials, and polytopes, Ann. of Math., 96 (1972), pp. 318-337. Zbl0237.14019MR304376
  11. [11] A.G. Kouchnirenko, Polyèdres de Newton et nombres de Milnor, Invent. Math., 32 (1976), pp. 1-31. Zbl0328.32007MR419433
  12. [12] P. Monsky, Finiteness of de Rham cohomology, Amer. J. Math., 94 (1972), pp. 237-245. Zbl0241.14010MR301017
  13. [13] V.P. Palamodov, Linear Differential Operators with Constant Coefficients, Springer-Verlag (1970). Zbl0191.43401MR264197
  14. [14] E. Spanier, Algebraic Topology, McGraw-Hill (1966). Zbl0145.43303MR210112

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