# William A. Stein

#14,466

Most Influential Person Now

American professor of mathematics

## William A. Stein's AcademicInfluence.com Rankings

William A. Steinmathematics Degrees

Mathematics

#783

World Rank

#1414

Historical Rank

#342

USA Rank

Measure Theory

#3194

World Rank

#3781

Historical Rank

#923

USA Rank

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Mathematics

## William A. Stein's Degrees

- PhD Mathematics University of California, Berkeley
- Bachelors Mathematics University of California, Berkeley

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## Why Is William A. Stein Influential?

(Suggest an Edit or Addition)According to Wikipedia, William Arthur Stein is a software developer and previously a professor of mathematics at the University of Washington. He is the lead developer of SageMath and founder of CoCalc. Stein does computational and theoretical research into the problem of computing with modular forms and the Birch and Swinnerton-Dyer conjecture. He is considered "a leading expert in the field of computational arithmetic".

## William A. Stein's Published Works

### Published Works

- Modular forms, a computational approach (2007) (369)
- SAGE: system for algebra and geometry experimentation (2005) (160)
- $J_1(p)$ has connected fibers (2003) (73)
- A Database of Elliptic Curves - First Report (2002) (59)
- Visible evidence for the Birch and Swinnerton-Dyer conjecture for modular abelian varieties of analytic rank zero (2004) (58)
- Computation of p-Adic Heights and Log Convergence (2006) (58)
- Explicit approaches to modular abelian varieties (2000) (55)
- Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves (2001) (54)
- The Manin Constant (2006) (53)
- Elementary Number Theory: Primes, Congruences, and Secrets (2009) (49)
- Average Ranks of Elliptic Curves: Tension between Data and Conjecture (2007) (45)
- Visibility of Shafarevich–Tate Groups of Abelian Varieties (2002) (43)
- Torsion points on elliptic curves over number fields of small degree (2016) (40)
- Computational verification of the Birch and Swinnerton-Dyer conjecture for individual elliptic curves (2009) (39)
- Lectures on Serre’s conjectures (2010) (34)
- Component Groups of Purely Toric Quotients (2001) (29)
- A Brief Introduction to Classical and Adelic Algebraic Number Theory (2004) (27)
- Prime Numbers and the Riemann Hypothesis (2016) (27)
- Fast computation of Hermite normal forms of random integer matrices (2010) (27)
- A mod five approach to modularity of icosahedral galois representations (2002) (26)
- SAGE: Software for Algebra and Geometry Experimentation (2006) (26)
- Elementary number theory : primes, congruences, and secrets : a computational approach (2009) (25)
- Algorithms for the arithmetic of elliptic curves using Iwasawa theory (2012) (25)
- Number Theory and Algebraic Geometry: Constructing elements in Shafarevich–Tate groups of modular motives (2004) (24)
- Lectures on Modular Forms and Hecke Operators (2011) (22)
- The modular degree, congruence primes, and multiplicity one (2012) (22)
- Shafarevich-Tate Groups of Nonsquare Order (2004) (22)
- Databases of elliptic curves ordered by height and distributions of Selmer groups and ranks (2016) (22)
- The Sage Project: Unifying Free Mathematical Software to Create a Viable Alternative to Magma, Maple, Mathematica and MATLAB (2010) (20)
- Some Computations with Heeke Rings and Deformation Rings (2002) (19)
- On the generation of the coefficient field of a newform by a single Hecke eigenvalue (2007) (19)
- Algebraic Number Theory, a Computational Approach (2010) (18)
- Elementary Number Theory (2008) (18)
- There are genus one curves over Q of every odd index (2003) (17)
- An introduction to computing modular forms using modular symbols (2008) (17)
- Component Groups of Quotients of J0(N) (2000) (17)
- The field generated by the points of small prime order on an elliptic curve (2001) (17)
- Modular Parametrizations of Neumann-Setzer Elliptic Curves (2004) (16)
- ANTS X: Proceedings of the Tenth Algorithmic Number Theory Symposium (2013) (15)
- Explicit Heegner Points: Kolyvagin's Conjecture and Non-trivial Elements in the Shafarevich-Tate Group (2007) (14)
- Cuspidal modular symbols are transportable (2001) (11)
- Computations About Tate-Shafarevich Groups Using Iwasawa Theory (2008) (10)
- Conjectures about Discriminants of Hecke Algebras of Prime Level (2004) (10)
- Verification of the Birch and Swinnerton - Dyer Conjecture for Specific Elliptic Curves (2005) (10)
- A p-adic analogue of the conjecture of Birch and Swinnerton-Dyer for modular abelian varieties (2012) (10)
- Visibility of the Shafarevich-Tate group at higher level (2007) (9)
- A database of elliptic curves over Q(sqrt 5): a first report (2012) (8)
- The Birch and Swinnerton-Dyer Conjecture , a Computational Approach (2007) (7)
- Studying the Birch and Swinnerton-Dyer conjecture for modular abelian varieties using Magma (2006) (7)
- The Manin Constant , Congruence Primes , and the Modular Degree (2005) (7)
- How Many Primes are There (2016) (7)
- Can we create a viable free open source alternative to magma, maple, mathematica and matlab? (2008) (7)
- Non‐commutative Iwasawa theory for modular forms (2012) (6)
- The Ring of Integers Modulo n (2009) (6)
- Modular forms of weight 2 (2007) (6)
- Foundations of Computational Mathematics, Budapest 2011: Sage: Creating a Viable Free Open Source Alternative to Magma, Maple, Mathematica, and MATLAB (2012) (6)
- p-adic heights of Heegner points and Λ-adic regulators (2014) (5)
- Explicitly Computing Modular Forms (2006) (4)
- Connections Between the Riemann Hypothesis and the Sato-Tate Conjecture (2008) (3)
- There are genus one curves over \mathbb{Q} of every odd index (2002) (3)
- Elementary Number Theory, A Computational Approach (2007) (3)
- On Power Bases in Number Fields (2005) (3)
- Heegner points and the arithmetic of elliptic curves over ring class extensions (2012) (3)
- Computing Tate-Shafarevich Groups of Elliptic Curves Using Iwasawa Theory (2011) (2)
- Visibility of Mordell-Weil groups (2007) (2)
- Toward a Generalization of the Gross–Zagier Conjecture (2010) (2)
- p-ADIC HEIGHTS OF HEEGNER POINTS AND ANTICYCLOTOMIC Λ-ADIC REGULATORS (2012) (2)
- Public-key Cryptography (2009) (1)
- What is Riemann's Hypothesis? (2016) (1)
- Some Abelian Varieties with Visible Shafarevich-Tate Groups (1999) (1)
- Has Connected Fibers (2003) (1)
- Open Source Mathematical Software: A White Paper (2008) (1)
- Numerical computation of Chow-Heegner points associated to pairs of elliptic curves ∗ † (2012) (1)
- Proving Mordell-Weil: A Descent in Three Parts (2005) (1)
- A Short Course on Galois Cohomology (2010) (1)
- Questions About Primes (2016) (1)
- - 0 EMPIRICAL EVIDENCE FOR THE BIRCH AND SWINNERTON-DYERCONJECTURES FOR MODULAR JACOBIANS OF GENUS 2 CURVESE (2001) (0)
- From the Riemann Spectrum to Primes (2016) (0)
- The Word “Spectrum” (2016) (0)
- The Mystery Moves to the Error Term (2016) (0)
- Further Questions About Primes (2016) (0)
- To Our Readers of Part I (2016) (0)
- Eisenstein series and Bernoulli numbers (2007) (0)
- Heegner Points on Rank Two Elliptic Curves (Preliminary Version) (2009) (0)
- Square Root Error and Random Walks (2016) (0)
- On Losing No Information (2016) (0)
- Spectra and Trigonometric Sums (2016) (0)
- In celebration of John Coates’ 60th birthday (2005) (0)
- As Riemann Envisioned It (2016) (0)
- A Sneak Preview of Part III (2016) (0)
- The Prime Number Theorem (2016) (0)
- Slopes of Graphs That Have No Slopes (2016) (0)
- AVERAGE RANKS OF ELLIPTIC CURVES (0)
- Some definitions of Hecke operators (2011) (0)
- How Many θi's are There? (2016) (0)
- Building π(X) from the Spectrum (2016) (0)
- Computer Music Files and Prime Numbers (2016) (0)
- What are Prime Numbers (2016) (0)
- The Staircase of Primes (2016) (0)
- General modular symbols (2007) (0)
- Tinkering with the Staircase of Primes (2016) (0)
- Prime Numbers Viewed from a Distance (2016) (0)
- Further Questions About the Riemann Spectrum (2016) (0)
- William A . Stein Detailed Research Plan Detailed Research Plan 1 Introduction (0)
- What is a “Good Approximation”? (2016) (0)
- A . 1 Colliot-Thelene 1 : Rational points on surfaces with a pencil of curves of genus one (0)
- Pure and Applied Mathematics (2016) (0)
- Sage Tutorial, Release 4.3.5 (2010) (0)
- Computing in higher rank (2007) (0)
- A Probabilistic First Guess (2016) (0)
- Fourier Transforms: Second Visit (2016) (0)
- A View of|Li(X)-π(X)| (2016) (0)
- Computing with newforms (2007) (0)
- Three Lectures about Explicit Methods in Number Theory Using Sage (2008) (0)
- Modular forms of level 1 (2007) (0)
- Fourier Transform of Delta (2016) (0)
- From Primes to the Riemann Spectrum (2016) (0)
- “Named” Prime Numbers (2016) (0)
- Thoughts About Numbers (2016) (0)
- Companions to the Zeta Function (2016) (0)
- Constructing Kolyvagin Classes : Kolyvagin ’ s Conjecture and Nontrivial Elements in the Shafarevich-Tate Group (2006) (0)
- The Spectrum and the Staircase of Primes (2016) (0)
- Hecke Algebras and Modular Forms: Notes derived from Ribet's 1996 Berkeley grad. course. (1998) (0)

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## What Schools Are Affiliated With William A. Stein?

William A. Stein is affiliated with the following schools: