Steven J. Miller                                                     
Assistant Professor of Mathematics, Williams College               
Bronfman Science Center (Steven.J.Miller AT williams.edu)    

  photos of Cam    Pictures    My Twistie Art  

curriculum vita
research statement
 teaching statement  
   Welcome letter to Williams Students
Possible thesis / colloquium projects
RESEARCH INTERESTS:  Analytic Number Theory, Random Matrix Theory, Analysis and Probability (distribution of zeros and n-level statistics for
families of L-functions, especially families of elliptic curves with rank over Q(T), classical random matrix theory, random graphs, ranks of elliptic curves, computational number theory, probability theory, Benford's Law, cryptography, linear programming, multiple Dirichlet series).

      Thesis         Papers        Talks     My Book (Invitation to Modern Number Theory)      Handouts      My Riddles Page

ACCEPTED  PAPERS

  1. 1- and 2-level densities for rational families of elliptic curves: evidence for the underlying group symmetries. Compositio Mathematica (140 (2004), no. 4, 952-992).    pdf
  2. Distribution of eigenvalues for the ensemble of real symmetric Toeplitz matrices (with Chris Hammond). Journal of Theoretical Probability (18 (2005), no. 3, 537-566).   pdf
  3. Benford's law, values of L-functions and the 3x+1 problem (with Alex Kontorovich), Acta Arithmetica. (120 (2005), no. 3, 269–297).  pdf.
  4. Variation in the number of points on elliptic curves and applications to excess rank, C. R. Math. Rep. Acad. Sci. Canada (27 (2005), no. 4, 111–120, Expanded Version). pdf
  5. Incomplete exponential sums in several variables (with Eduardo Dueñez, Howard Straubing, and Amitahba Roy), Journal of Number Theory (116 (2006), no. 1, 168–199). pdf
  6. A derivation of James' Pythagorean projection, By The Numbers -- The Newsletter of the SABR Statistical Analysis Committee (16 (February 2006), no. 1, 17–22).   pdf (expanded version: pdf).  Chance Magazine (20 (Winter 2007), no. 1, 40-48).
  7. Investigations of zeros near the central point of elliptic curve L-functions, Experimental Mathematics (15 (2006), no. 3, 257–279).  pdf  (data available online).
  8. Closed-form Bayesian inferences for the logit model via polynomial expansions (with Eric Bradlow and Kevin Dayaratna), Quantitative Marketing and Economics (4 (2006), no. 2, 173–206).   pdf
  9. Low-lying zeros of L-functions with orthogonal symmetry (with Chris Hughes), Duke Mathematical Journal (136 (2007), no. 1, 115–172)   pdf
  10. The low-lying zeros of a GL(4) and a GL(6) family of L-functions (with Eduardo Dueñez), Compositio Mathematica (142 (2006), no. 6, 1403–1425) pdf.
  11. Constructing one-parameter families of elliptic curves over Q(T) with moderate rank (with Scott Arms, Alvaro Lozano-Robledo), Journal of Number Theory. (123 (2007), no 2, 388–402   pdf
  12. Benford's Law applied to hydrology data - results and relevance to other geophysical data (with Mark Nigrini), Mathematical Geology, (39 (2007), no. 5, 469--490).
  13. Distribution of eigenvalues of real symmetric palindromic Toeplitz matrices and circulant matrices (with Adam Massey and John Sinsheimer), Journal of Theoretical Probability. (20 (2007), no. 3, 637--662.)  pdf
  14. When the Cramer-Rao Inequality provides no information, Communications in Information and Systems.  (7 (2007), no. 3, 265--272).   pdf
  15. The Modulo 1 Central Limit Theorem and Benford's Law for Products (with Mark Nigrini), International Journal of Algebra. (2 (2008), no. 3, 119--130). pdf
  16. A Symplectic Test of the L-Functions Ratios Conjecture, IMRN (2008). (Vol. 2008, article ID rnm146, 36 pages, doi:10.1093/imrn/rnm146).   pdf
  17. An identity for sums of polylogarithm functions, Integers (electronic journal of combinatorial number theory). (8 (2008), A15)   pdf
  18. A probabilistic proof of Wallis' formula for π, American Mathematical Monthly. (115 (2008), no. 8, 740--745)   pdf
  19. The distribution of the second largest eigenvalue in families of random regular graphs (with Tim Novikoff and Anthony Sabelli), Experimental Mathematics. (17 (2008), no. 2, 231--244.)  pdf
  20. Silver Scheduler: Demand-Driven Scheduling of Movies in a Multiplex (with Jehoshua Eliashberg, Quintus Hegie, Jason Ho, Dennis Huisman, Sanjeev Swami, Charles B. Weinberg and Berend Wierenga), to appear in the International Journal of Market Research.   pdf
  21. Order statistics and Benford's law (with Mark Nigrini), to appear in the International Journal of Mathematics and Mathematical Sciences.  pdf
  22. When almost all sets are difference dominated (with Peter Hegarty), to appear in Random Structures and Algorithms.   pdf 
  23. Lower order terms in the 1-level density for families of holomorphic cuspidal newforms, to appear in Acta Arithmetica. pdf

SUBMITTED  PAPERS

  1. The effect of convolving families of L-functions on the underlying group symmetries (with Eduardo Dueñez), submitted to Proc. of the LMS.   pdf
  2. Advanced tests based on Benford's Law to test the reliability of and control risk pertaining to accounting data (with Mark Nigrini), submitted to Auditing: A Journal of Practice and Theory.
  3. An orthogonal test of the L-functions Ratios Conjecture, submitted to the London Mathematical Society.   pdf
  4. Explicit constructions of infinite families of MSTD sets (with Brooke Orosz and Dan Scheinerman), submitted to the Journal of Number Theory. pdf

PREPRINTS / IN  PREPARATION.

  1. Chains of distributions, hierarchical Bayesian models and Benford's Law (with D. Jang, J. U. Kang, A. Kruckman and J. Kudo)   pdf
  2. 1-Level Density for Square-Free Dirichlet Characters.    pdf
  3. Using the 2-Level Density to Improve Bounds on Excess Rank in Families.   pdf
  4. m-Paths and the 3x+1 Problem (with Bruce Adcock and Sucheta Soundararajan).
  5. Virus Propagation in Certain Types of Networks (with Leo Kontorovich and Amitabha Roy).
  6. Models for zeros near the central point of families of elliptic curves (with Eduardo Dueñez, Duc Khiem Huynh, Jon Keating and Nina Snaith).

      Thesis         Papers        Talks     My Book (Invitation to Modern Number Theory)      Handouts      My Riddles Page

COURSES:     Welcome letter to Williams Students    Possible thesis / colloquium projects   Green Chicken contest
          2008 - 2009: Math 103 (Calculus I)       Math 209 (Differential Equations and Vector Calculus)    Math 406 (Analysis and Number Theory)
          Previous classes (Brown): Math 1 (freshman seminar: riddles to modern mathematics), Math 90 (calculus, summer calculus)
                                                  Math 35 (honors multivariable calculus), Math 52 (linear algebra)   Math 54 (honors linear algebra),    Math 153 (abstract algebra),
                                        Math 162 (mathematical statistics), Math 197 (Benford's law, sabermetrics)
          Previous Classes (Ohio State) Math 104 (Basic College Mathematics), Math 148 (Algebra, Trigonometry and their Applications)
                                        Math 187/487 (Problem Solving / Advanced Problem Solving), Math 683L (Topics in Linear Algebra)
                                                  Working groups (Euler, fractals)
 

LINKS:    photos of Cam  Pictures  Twistie Art Arxiv     MathSciNet  Mathlabs (Princeton , NYU, OSU,  AIM) Williams Math Williams College