Steven J

Steven J. Miller
Assistant Professor of Mathematics, Brown University
210 Kassar House, 401-863-1123 (sjmiller AT math.brown.edu)

Starting in Fall '08 I will be an assistant professor of mathematics and statistics at Williams College. I can always be reached at Steven.Miller.MC.96 AT aya.yale.edu

curriculum vita
research statement
teaching statement

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 (An Invitation to Modern Number Theory) Handouts My Riddles Page

ACCEPTED PAPERS

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
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
Benford's law, values of L-functions and the 3x+1 problem (with Alex Kontorovich), Acta Arithmetica. (120 (2005), no. 3, 269–297). pdf.
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
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
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).
Investigations of zeros near the central point of elliptic curve L-functions, Experimental Mathematics (15 (2006), no. 3, 257–279). pdf (data available online).
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
Low-lying zeros of L-functions with orthogonal symmetry (with Chris Hughes), Duke Mathematical Journal (136 (2007), no. 1, 115–172) pdf
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.
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
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).
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
When the Cramer-Rao Inequality provides no information, Communications in Information and Systems. (7 (2007), no. 3, 265--272). pdf
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
A Symplectic Test of the L-Functions Ratios Conjecture, IMRN (2008). (Vol. 2008, article ID rnm146, 36 pages, doi:10.1093/imrn/rnm146). pdf
An identity for sums of polylogarithm functions, Integers (electronic journal of combinatorial number theory). (8 (2008), A15) pdf
A probabilistic proof of Wallis' formula for π, to appear in the American Mathematical Monthly. pdf
The distribution of the second largest eigenvalue in families of random regular graphs (with Tim Novikoff and Anthony Sabelli), to appear in Experimental Mathematics. pdf

SUBMITTED PAPERS

The effect of convolving families of L-functions on the underlying group symmetries (with Eduardo Dueñez), submitted to Crelle's Journal. pdf
Order statistics and Benford's law (with Mark Nigrini). International Journal of Mathematics and Mathematical Sciences. pdf
Lower order terms in the 1-level density for families of holomorphic cuspidal newforms, submitted to Acta Arithmetica. pdf
When almost all sets are difference dominated (with Peter Hegarty), submitted to Random Structures and Algorithms. pdf (expanded version)
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.
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), submitted to International Journal of Market Research. pdf

PREPRINTS / IN PREPARATION

An orthogonal test of the L-functions Ratios Conjecture. pdf
Chains of distributions, hierarchical Bayesian models and Benford's Law (with D. Jang, J. U. Kang, A. Kruckman and J. Kudo). pdf
1-Level Density for Square-Free Dirichlet Characters. pdf
Using the 2-Level Density to Improve Bounds on Excess Rank in Families. pdf
m-Paths and the 3x+1 Problem (with Bruce Adcock and Sucheta Soundararajan).
Virus Propagation in Certain Types of Networks (with Leo Kontorovich and Amitabha Roy).
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 (An Invitation to Modern Number Theory) Handouts My Riddles Page