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Rank one case of Dwork's conjecture
Author(s):
Daqing
Wan
Journal:
J. Amer. Math. Soc.
13
(2000),
853-908.
MSC (2000):
Primary 11G40, 11S40;
Secondary 11M41, 11G25
Posted:
June 6, 2000
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Abstract:
In this paper, we prove the rank one case of Dwork's conjecture on the  -adic meromorphic continuation of the pure slope L-functions arising from the slope decomposition of an overconvergent F-crystal. Further explicit information about zeros and poles of the pure slope L-functions are also obtained, including an application to the Gouvêa-Mazur type conjecture in this setting.
References:
-
- 1.
- P. Berthelot, Cohomologie rigide et cohomologie rigide à supports propres, Prépublication 96-03, Institut de Recherche Mathématique de Rennes.
- 2.
- R. Coleman,
 -Adic Banach spaces and families of modular forms, Invent. Math., 127(1997), 417-479. MR 98b:11047 - 3.
- R. Coleman and B. Mazur, The eigencurve, in Galois Representations in Arithmetic Algebraic Geometry (Durham, 1996), London Math. Soc. Lecture Note Ser., 254, 1998, 1-113. CMP 99:15
- 4.
- B. Dwork, Normalized period matrices, Ann. Math., 94(1971), 337-388. MR 53:442a
- 5.
- B. Dwork, Normalized period matrices II, Ann. Math., 98(1973), 1-57. MR 53:442b
- 6.
- F. Gouvêa and B. Mazur, Families of modular eigenforms, Math. Comp., 58(1992), 793-806. MR 93d:11049
- 7.
- F. Gouvêa and B. Mazur, On the characteristic power series of the
 operator, Ann. Inst. Fourier, Grenoble, 43(1993), 301-302. MR 94c:11039 - 8.
- N. Katz, Travaux de Dwork, Séminaire Bourbaki, exposé 409(1971/72), Lecture Notes in Math., No. 317, 1973, 167-200. MR 58:16672
- 9.
- N. Katz, Slope filtration of F-crystals, Astérisque, 63(1979), 113-164. MR 81i:14014
- 10.
- P. Monsky, Formal cohomology III, Ann. Math., 93(1971), 315-343. MR 48:296
- 11.
- J-P. Serre, Endomorphismes complètement continus des espaces de Banach
 -adiques, Publ. Math., IHES, 12(1962), 69-85. MR 26:1733 - 12.
- D. Wan, Newton polygons of zeta functions and L-functions, Ann. Math., 137(1993), 247-293. MR 94f:11074
- 13.
- D. Wan, Noetherian subrings of power series rings, Proc. Amer. Math. Soc., 123(1995), 1681-1686. MR 95g:13021
- 14.
- D. Wan, Meromorphic continuation of L-functions of
 -adic representations, Ann. Math., 143(1996), 469-498. MR 97c:14021 - 15.
- D. Wan, Dimension variation of classical and
 -adic modular forms, Invent. Math., 133(1998), 449-463. MR 99d:11039 - 16.
- D. Wan, Dwork's conjecture on unit root zeta functions, Ann. Math., 150(1999), 867-927. CMP 2000:08
- 17.
- D. Wan, Higher rank case of Dwork's conjecture, J. Amer. Math. Soc., this issue.
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Additional Information:
Daqing
Wan
Affiliation:
Department of Mathematics, University of California, Irvine, California 92697
Email:
dwan@math.uci.edu
DOI:
10.1090/S0894-0347-00-00340-4
PII:
S 0894-0347(00)00340-4
Keywords:
L-functions,
Fredholm determinants,
$p$-adic meromorphic continuation,
nuclear $\sigma$-modules,
Banach modules
Received by editor(s):
June 28, 1999
Received by editor(s) in revised form:
April 10, 2000
Posted:
June 6, 2000
Additional Notes:
This work was partially supported by the National Science Foundation
Copyright of article:
Copyright
2000,
American Mathematical Society
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