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Karl Rubin: preprints & reprints

Word frequency cloud for the titles of my papers, made using http://www.wordle.net

Papers on the arXiv


preprints:

(with B. Mazur) Controlling Selmer groups in the higher core rank case.

(with B. Mazur) Refined class number formulas for Gm.

(with B. Mazur, and an appendix by M. Larsen) Diophantine stability.


reprints available on the internet (some may require subscriptions):

(with B. Mazur) Selmer companion curves. Transactions Amer. Math. Soc. 367 (2015) 401-421.

(with Z. Klagsbrun and B. Mazur) A Markov model for Selmer ranks in families of twists. Compositio Math. 150 (2014) 1077-1106.

(with R. Greenberg, A. Silverberg, and M. Stoll) On elliptic curves with an isogeny of degree 7. American J. Math. 136 (2014) 77-109.

(with J. B. Friedlander, H. Iwaniec, and B. Mazur) The spin of prime ideals. Inventiones math. 193 (2013) 697-749.

(with Z. Klagsbrun and B. Mazur) Disparity in Selmer ranks of quadratic twists of elliptic curves. Annals of Math. 178 (2013) 287-320.

(with D. Boneh and A. Silverberg) Finding composite order ordinary elliptic curves using the Cocks-Pinch method. Journal of Number Theory 131 (2011) 832-841.

(with B. Mazur) Refined class number formulas and Kolyvagin systems. Compositio Mathematica 147 (2011) 54-76.

(with B. Mazur) Ranks of twists of elliptic curves and Hilbert's Tenth Problem. Inventiones mathematicae 181 (2010) 541-575.

(with A. Silverberg) Choosing the correct elliptic curve in the CM method. Mathematics of Computation 79 (2010) 545-561.

(with A. Silverberg) Point counting on reductions of CM elliptic curves. Journal of Number Theory 129 (2009) 2903-2923.

(with A. Silverberg) Using abelian varieties to improve pairing-based cryptography. Journal of Cryptology 22 (2009) 330-364.

(with B. Mazur) Growth of Selmer rank in nonabelian extensions of number fields. Duke Math. Journal 143 (2008) 437-461.

(with A. Silverberg) Compression in finite fields and torus-based cryptography. SIAM Journal on Computing 37 (2008) 1401-1428.

(with B. Mazur) Finding large Selmer rank via an arithmetic theory of local constants. Annals of Mathematics 166 (2007) 581-614.

(with B. Mazur and A. Silverberg) Twisting commutative algebraic groups. Journal of Algebra 314 (2007) 419-438.

(with A. Silverberg) Twists of elliptic curves of rank at least four. In: Ranks of elliptic curves and random matrix theory, Conrey et al., eds., London Math. Soc. Lecture Notes 341 (2007) 177-188.

Fudge factors in the Birch and Swinnerton-Dyer conjecture. In: Ranks of elliptic curves and random matrix theory, Conrey et al., eds., London Math. Soc. Lecture Notes 341 (2007) 233-236.

Appendix to: Anticyclotomic Iwasawa theory of CM elliptic curves, by A. Agboola and B. Howard. Annales de l'Institut Fourier 56 (2006) 1001-1048.

(with B. Mazur) Finding large Selmer groups. J. Differential Geometry 70 (2005) 1–22

(with B. Mazur) Organizing the arithmetic of elliptic curves. Advances in Math. 198 (2005) 504-546.

(with M. van Dijk, R. Granger, D. Page, A. Silverberg, M. Stam, D. Woodruff) Practical cryptography in high dimensional tori. In: Advances in Cryptology - EUROCRYPT 2005. Lect. Notes in Comp. Sci. 3494 (2005) 234-250.

(with R. Pollack) The main conjecture for CM elliptic curves at supersingular primes. Ann. of Math. 159 (2004) 447-464.

(with A. Silverberg) Using primitive subgroups to do more with fewer bits. In: Algorithmic Number Theory - ANTS VI. Lect. Notes in Comp. Sci. 3076 (2004) 18-41.

(with B. Mazur) Studying the Growth of Mordell-Weil. Doc. Math. Extra volume: Kato's Fiftieth Birthday (2003) 585-607.

(with A. Silverberg) Torus-based cryptography. In: Advances in Cryptology - CRYPTO 2003. Lect. Notes in Comp. Sci. 2729 (2003) 349-365.

(with B. Mazur) Elliptic curves and class field theory. Proceedings of the ICM, Beijing 2002 vol. 2, 185-196.

(with A. Silverberg) Ranks of elliptic curves. Bull. Amer. Math. Soc. 39 (2002) 455-474.

(with A. Silverberg) Supsersingular abelian varieties in cryptology. In: Advances in Cryptology - CRYPTO 2002. Lect. Notes in Comp. Sci. 2442 (2002) 336-353.

(with A. Silverberg) Rank frequencies for quadratic twists of elliptic curves. Exp. Math. 10 (2001) 559-569.

(with A. Silverberg) Mod 2 representations of elliptic curves. Proc. Amer. Math. Soc. 129 (2001) 53-57.

(with A. Silverberg) Ranks of elliptic curves in families of quadratic twists. Exp. Math. 9 (2000) 583-590.

A Stark conjecture "over Z" for abelian L-functions with multiple zeros. Annales de l'institut Fourier 46 (1996) 33-62.

(with A. Silverberg) A report on Wiles' Cambridge lectures. Bull. Amer. Math. Soc. 31 (1994) 15-38.

p-adic L-functions and rational points on elliptic curves with complex multiplication. Invent. Math. 107 (1992) 323-350.

The "main conjectures" of Iwasawa theory for imaginary quadratic fields. Invent. Math. 103 (1991) 25-68.

On the main conjecture of Iwasawa theory for imaginary quadratic fields. Invent. Math. 93 (1988) 701-713.

Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication. Invent. Math. 89 (1987) 527-559.

Global units and ideal class groups. Invent. Math. 89 (1987) 511-526.

Local units, elliptic units, Heegner points and elliptic curves. Invent. Math. 88 (1987) 405-422.

Congruences for special values of L-functions of elliptic curves with complex multiplication. Invent. Math. 71 (1983) 339-364.

Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer. Invent. Math. 64 (1981) 455-470.