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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Diophantine equations and congruences over function fields

Author(s): Elena Yudovina
Journal: Proc. Amer. Math. Soc. 136 (2008), 3839-3850.
MSC (2000): Primary 11D45
Posted: June 3, 2008
MathSciNet review: 2425723
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Abstract | References | Similar articles | Additional information

Abstract: We generalize the methods of Pierce for counting solutions to the congruence $ X^a \equiv Y^b \bmod D$ and the square sieve method for counting squares in the sequence $ f(X) + g(Y)$

to the function field setting.


References:

1.
J. Ellenberg and A. Venkatesh, Reflection principles and bounds for class group torsion. Int. Math. Res. Not. IMRN 2007, no. 1, Art. ID #rnm002. MR 2331900

2.
D. R. Heath-Brown, Hybrid bounds for $ L$-functions: a $ q$-analogue of Van der Corput's method and a $ t$-analogue of Burgess's method. Recent Progress in Analytic Number Theory, eds. Halberstam and Hooley. Academic Press, London (1981), pp. 121-126.

3.
D. R. Heath-Brown, The least square-free number in an arithmetic progression. J. Reine Angew. Math. 332 (1982) 204-220. MR 656864 (83i:10057)

4.
H. Helfgott and A. Venkatesh, Integral points on elliptic curves and 3-torsion in class groups. J. Amer. Math. Soc. 19, no. 3 (2005) 527-550. MR 2220098 (2007b:11081)

5.
C. Hooley, A note on square-free numbers in arithmetic progressions. Bull. London Math. Soc. 7 (1975) 133-138. MR 0371799 (51:8016)

6.
N. M. Katz, On a question of Lillian Pierce. Forum Math. 18 (2006) 699-710. MR 2254391

7.
L. B. Pierce, A bound for the 3-part of class numbers of quadratic fields by means of the square sieve. Forum Math. 18 (2006) 677-698. MR 2254390

8.
L. B. Pierce, The 3-part of class numbers of quadratic fields. J. London Math. Soc. (2) 71 (2005) 579-598. MR 2132372 (2006e:11167)

9.
M. Rosen, Number Theory in Function Fields, Graduate Texts in Mathematics, 210, Springer, Berlin (2000). MR 1876657 (2003d:11171)

10.
W. Schmidt, Equations over finite fields: an elementary approach, Lecture Notes in Mathematics, 536, Springer, Berlin (1976). MR 0429733 (55:2744)


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Additional Information:

Elena Yudovina
Affiliation: Department of Mathematics, FAS, Harvard University, One Oxford Street, Cambridge, Massachusetts 02138

DOI: 10.1090/S0002-9939-08-09363-5
PII: S 0002-9939(08)09363-5
Received by editor(s): July 25, 2007,
Received by editor(s) in revised form: October 2, 2007
Posted: June 3, 2008
Communicated by: Ken Ono
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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