Karl Rubin | Academic Influence

Karl Rubin's AcademicInfluence.com Rankings

Karl Rubin

Mathematics

#1649

World Rank

#2656

Historical Rank

#672

USA Rank

Number Theory

#75

World Rank

#108

Historical Rank

#17

USA Rank

Measure Theory

#3367

World Rank

#3977

Historical Rank

#969

USA Rank

mathematics Degrees

Download Badge

Mathematics

Karl Rubin's Degrees

PhD Mathematics University of California, Berkeley
Bachelors Mathematics Princeton University

Similar Degrees You Can Earn

Best Online Bachelor's in Math 2025

Why Is Karl Rubin Influential?

(Suggest an Edit or Addition)

According to Wikipedia, Karl Cooper Rubin is an American mathematician at University of California, Irvine as Thorp Professor of Mathematics. Between 1997 and 2006, he was a professor at Stanford, and before that worked at Ohio State University between 1987 and 1999. His research interest is in elliptic curves. He was the first mathematician to show that some elliptic curves over the rationals have finite Tate–Shafarevich groups. It is widely believed that these groups are always finite.

(See a Problem?)

Karl Rubin's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

The “main conjectures” of iwasawa theory for imaginary quadratic fields (1988) (372)
A Stark conjecture “over ${\bf Z}$” for abelian $L$-functions with multiple zeros (1996) (150)
Tate-Shafarevich groups andL-functions of elliptic curves with complex multiplication (1987) (146)
Ranks of twists of elliptic curves and Hilbert’s tenth problem (2009) (133)
Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer (1981) (125)
Torus-Based Cryptography (2003) (124)
Supersingular Abelian Varieties in Cryptology (2002) (112)
Ranks of elliptic curves (2002) (90)
Finding Large Selmer Rank via an Arithmetic Theory of Local Constants (2005) (77)
On the main conjecture of Iwasawa theory for imaginary quadratic fields (1988) (66)
Global units and ideal class groups (1987) (63)
p-adicL-functions and rational points on elliptic curves with complex multiplication (1992) (51)
Twisting Commutative Algebraic Groups (2006) (51)
The main conjecture for CM elliptic curves at supersingular primes (2005) (49)
Stark units and Kolyvagin's „Euler Systems“ (1992) (48)
Practical Cryptography in High Dimensional Tori (2005) (47)
Arithmetic Algebraic Geometry (2008) (47)
Finding composite order ordinary elliptic curves using the Cocks-Pinch method (2011) (46)
Rank Frequencies for Quadratic Twists of Elliptic Curves (2000) (46)
Swan Modules and Hilbert–Speiser Number Fields (1999) (45)
Choosing the correct elliptic curve in the CM method (2010) (41)
Galois Representations in Arithmetic Algebraic Geometry: Euler systems and modular elliptic curves (1998) (41)
Using Abelian Varieties to Improve Pairing-Based Cryptography (2009) (37)
Using Primitive Subgroups to Do More with Fewer Bits (2004) (35)
Review: Ehud de Shalit, Iwasawa theory of elliptic curves with complex multiplication (1989) (35)
Mod 2 representations of elliptic curves (1999) (32)
Kolyvagin’s System of Gauss Sums (1991) (30)
Compression in Finite Fields and Torus-Based Cryptography (2008) (30)
More “Main conjectures” for imaginary quadratic fields (1994) (30)
The spin of prime ideals (2011) (28)
Congruences for special values ofL-functions of elliptic curves with complex multiplication (1983) (25)
Diophantine stability (2015) (25)
Controlling Selmer groups in the higher core rank case (2013) (24)
Elliptic curves and class field theory (2003) (24)
Refined class number formulas and Kolyvagin systems (2009) (22)
Organizing the arithmetic of elliptic curves (2005) (22)
Refined class number formulas for Gm (2016) (22)
A report on Wiles’ Cambridge lectures (1994) (22)
Refined class number formulas for Gm (2016) (22)
A Markov model for Selmer ranks in families of twists (2013) (21)
Local units, elliptic units, Heegner points and elliptic curves (1987) (21)
Ranks of Elliptic Curves in Families of Quadratic Twists (1999) (21)
Abelian varieties, p-adic heights and derivatives (1994) (20)
Arithmetic Conjectures Suggested by the Statistical Behavior of Modular Symbols (2019) (20)
Tate–Shafarevich Groups of Elliptic Curves with Complex Multiplication (1989) (19)
Point counting on reductions of CM elliptic curves (2007) (19)
Growth of Selmer rank in nonabelian extensions of number fields (2007) (18)
Studying the Growth of Mordell-Weil (2003) (18)
MODULARITY OF MOD 5 REPRESENTATIONS (1997) (17)
Criteria for complete intersections (1997) (17)
The work of kolyvagin on the arithmetic of elliptic curves (1989) (15)
Disparity in Selmer ranks of quadratic twists of elliptic curves (2011) (15)
Ranks of Elliptic Curves and Random Matrix Theory: Twists of elliptic curves of rank at least four (2007) (14)
Refined class number formulas for $\mathbb{G}_m$ (2013) (12)
FINDING LARGE SELMER GROUPS (2005) (12)
Mordell-Weil Groups of Elliptic Curves Over Cyclotomic Fields (1982) (11)
L-functions and Arithmetic: The one-variable main conjecture for elliptic curves with complex multiplication (1991) (11)
The best and worst of supersingular abelian varieties in cryptology (2002) (9)
Elliptic curves and $\mathbb {Z}_p$-extensions (1985) (7)
Selmer companion curves (2012) (6)
Ranks of Elliptic Curves and Random Matrix Theory: Fudge Factors in the Birch and Swinnerton-Dyer Conjecture (2007) (6)
Erratum to: The spin of prime ideals (2015) (5)
Pairings in the Arithmetic of Elliptic Curves (2004) (5)
Arithmetic theory of elliptic curves : lectures given at the 3rd session of the Centro internazionale matematico estivo (C.I.M.E.), held in Cetraro, Italy, July 12-19, 1997 (1999) (4)
Arithmetic of -functions (2011) (3)
Euler systems and Kolyvagin systems (2009) (3)
Existential definability and diophantine stability (2022) (2)
Big fields that are not large (2020) (2)
Advances in Cryptology – EUROCRYPT 2019 (2019) (1)
Number of Cycles of Length Four in Sum Graphs and Integral Sum Graphs (2014) (1)
Arithmetic of L-Functions (2011) (1)
Descents on elliptic curves with complex multiplication (1987) (1)
Ranks of elliptic curves over Q(t) with constant j-invariant (2000) (0)
List of speakers and schedule (2012) (0)
Chapter 9. Variants (2000) (0)
Erratum: “A report on Wiles’ Cambridge lectures” [Bull.\ Amer.\ Math.\ Soc.\ (N.S.)\ {31} (1994), no.\ 1, 15–38; MR1256978 (94k:11062)] by K. Rubin and A. Silverberg (1995) (0)
Table of A (k) (n) (1974) (0)
Book Review: $p$-Adic $L$-functions and $p$-adic representations (2002) (0)
Review of " Euler Systems " by Karl Rubin (2007) (0)
Chapter 3. Examples and Applications (2000) (0)
Appendix D. p-adic Calculations in Cyclotomic Fields (2000) (0)
Chapter 4. Derived Cohomology Classes (2000) (0)
Chapter 6. Twisting (2000) (0)
Chapter 1. Galois Cohomology of p-adic Representations (2000) (0)
Chapter 8. Euler Systems and p-adic L-functions (2000) (0)
Defining $\mathbb Z$ using unit groups (2023) (0)
Contemporary Mathematics Introduction to Kolyvagin systems (2003) (0)
Chapter 5. Bounding the Selmer Group (2000) (0)
The spin of prime ideals (2012) (0)
Appendix B. Continuous Cohomology and Inverse Limits (2000) (0)
Journées Arithmétiques 1980: Iwasawa theory and elliptic curves: supersingular primes (1982) (0)
Appendix C. Cohomology of p-adic Analytic Groups (2000) (0)
A “BASIC NOTIONS” LECTURE ABOUT SIGN INTUITIONS (2006) (0)
Erratum to: The spin of prime ideals (2015) (0)
Chapter 2. Euler Systems: Definition and Main Results (2000) (0)
This paper was presented at a colloquium entitled “ Elliptic Curves and Modular Forms , ” organized by (1997) (0)
Algebraic maps constant on isomorphism classes of unpolarized abelian varieties are constant (2019) (0)
Chapter 7. Iwasawa Theory (2000) (0)
Appendix A. Linear Algebra (2000) (0)

This paper list is powered by the following services:

Other Resources About Karl Rubin

What Schools Are Affiliated With Karl Rubin?

Karl Rubin is affiliated with the following schools:

Image Attributions

Image Source for Karl Rubin