On characteristic p zeta functions

Dinesh S. Thakur

Compositio Mathematica (1995)

  • Volume: 99, Issue: 3, page 231-247
  • ISSN: 0010-437X

How to cite

top

Thakur, Dinesh S.. "On characteristic $p$ zeta functions." Compositio Mathematica 99.3 (1995): 231-247. <http://eudml.org/doc/90415>.

@article{Thakur1995,
author = {Thakur, Dinesh S.},
journal = {Compositio Mathematica},
keywords = {characteristic zeta functions; estimates; Drinfeld modules; lower bound on the order of the zeros; Dedekind zeta functions; trivial zeros; orders of vanishing},
language = {eng},
number = {3},
pages = {231-247},
publisher = {Kluwer Academic Publishers},
title = {On characteristic $p$ zeta functions},
url = {http://eudml.org/doc/90415},
volume = {99},
year = {1995},
}

TY - JOUR
AU - Thakur, Dinesh S.
TI - On characteristic $p$ zeta functions
JO - Compositio Mathematica
PY - 1995
PB - Kluwer Academic Publishers
VL - 99
IS - 3
SP - 231
EP - 247
LA - eng
KW - characteristic zeta functions; estimates; Drinfeld modules; lower bound on the order of the zeros; Dedekind zeta functions; trivial zeros; orders of vanishing
UR - http://eudml.org/doc/90415
ER -

References

top
  1. [A1] Anderson, G.: Rank one elliptic A-modules and A-harmonic series, Duke Math. J.73 (1994) 491-542. Zbl0807.11032MR1262925
  2. [A-T] Anderson G. and Thakur D.: Tensor powers of the Carlitz module and zeta values, Annals of Math.132 (1990) 159-191. Zbl0713.11082MR1059938
  3. [C1] Carlitz L.: On certain functions connected with polynomials in a Galois field, Duke Math. J.1 (1935) 137-168. Zbl0012.04904MR1545872JFM61.0127.01
  4. [G1] Goss D.: v-adic zeta functions, L-series and measures for function fields, Inventiones Mathematicae55 (1979) 107-119. Zbl0413.12009MR553704
  5. [G2] Goss D.: The theory of totally real function fields, Contemp. Math. vol. 55, Amer. Math. Soc. Providence, R. I. (1986) 449-477. Zbl0602.14029MR862648
  6. [G3] Goss D.: Analogies between global fields, Conference Proceedings, Canadian Mathematical Society7 (1987) 83-114. Zbl0619.12009MR894321
  7. [G4] Goss D.: L-series of t motives, The Arithmetic of function fields, Ed. Goss D. et al, Walter de Gruyter, NY (1992) 313-402. Zbl0806.11028MR1196527
  8. [K] Klingen H.: Uber die werte der Dedekndschen zetafunktion, Math. Annalen145 (1962) 265-272. Zbl0101.03002MR133304
  9. [L1] Lee H.: Power sums of polynomials in a Galois field, Duke Math J.10 (1943) 277-292. Zbl0063.03468MR8074
  10. [H1] Hayes D.: Explicit class field theory in global function fields, Studies in Algebra and Number theory - Ed. G. C. Rota, Academic press (1979) 173-217. Zbl0476.12010MR535766
  11. [H2] Hayes D.: A brief introduction to Drinfeld modules, The Arithmetic of Function Fields, Ed. David Goss et al, Walter de Gruyter, NY (1992) 1-32. Zbl0793.11015MR1196509
  12. [T1] Thakur D.: Gamma functions and Gauss sums for function fields and periods of Drinfeld modules, Thesis, Harvard University, (1987). Zbl0734.11036
  13. [T2] Thakur D.: Zeta measure associated to Fq[T], J. Number Theory35 (1990) 1-17. Zbl0703.11065MR1054555
  14. [T3] Thakur D.: Gauss sums for function fields, J. Number Theory37 (1991) 242-252. Zbl0716.11057MR1092609
  15. [T4] Thakur D.: Drinfeld modules and arithmetic in function fields, International Mathematics Research Notices1992, No. 9, 185-197, Duke Math. J.68 (1992). Zbl0756.11015MR1185833
  16. [T5] Thakur D.: Iwasawa theory and cyclotomic function fields, Proceedings of the conference on Arithmetic geometry, March 93, Ed. N. Childress, J. Jones, Contemporary Math., vol. 174 (1994), American Math. Soc., 157-165. Zbl0811.11043MR1299741
  17. [Y1] Yu J.: Transcendence and special zeta values in characteristic p, Ann. Math.134 (1991) 1-23. Zbl0734.11040MR1114606

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.