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CORRIGENDUM TO “GALOIS REPRESENTATIONS ATTACHED TO Q-CURVES AND THE GENERALIZED FERMAT EQUATION A4 + B2 = Cp” By JORDAN S. ELLENBERG In [1], the author proved that the equation A4 + B2 = Cp has no solutions in integers providing that A, B, C are coprime nonzero integers and p ≥ 211. The precise bound on p depended on the results of [2]. Some changes in the latter paper after publication of [1] necessitate corresponding changes in some of the numerical computations in Section 4 of [1]. These changes do not affect the truth of any theorem of [1]. The changes, all on page 785, are as follows: • In the inequality |(a1, Lχ)p2 − 4π| ≤ 4.37, change 4.37 to 4.66. • “At level p, the same theorem gives |(a1, Lχ)p| ≤ 786” should be replaced by “The argument of Lemma 3.13 applies word for word with amp replaced by am, showing that |(a1, Lχ)p| ≤ 437.” • The last inequality on the page should thus read|(a1, Lχ)p−new| ≥ 4π − 4.66 − 211 2112 − 1 (437 + 437/211) > 5. DEPARTMENT OF MATHEMATICS, UNIVERSITY OF WISCONSIN, MADISON, WI, 53706-1388 E-mail: ellenber@math.wisc.edu REFERENCES [1] J. Ellenberg, Galois representations attached to Q-curves and the generalized Fermat equation A4 + B2 = Cp, Amer. J. Math. 126(4), 763–787, 2004. [2] , On the error term in Duke’s estimate for the average special value of L-functions, Canad. Math. Bull. (to appear). Manuscript received April 21, 2005; revised July 1, 2005. Research supported in part by NSF Grant DMS-0401616. American Journal of Mathematics 127 (2005), 1389. 1389 ...

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
p. 1389
Launched on MUSE
2005-12-12
Open Access
No
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