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Distribution of Eigenvalues for the Ensemble of Real Symmetric Toeplitz Matrices
- Christopher N. B. Hammond, S. Miller
- Mathematics
- 1 July 2005
AbstractConsider the ensemble of real symmetric Toeplitz matrices whose entries are
i.i.d. random variable from a fixed probability distributionpof mean 0,variance 1, and finite moments of all order.…
An Invitation to Modern Number Theory
- S. Miller, Ramin Takloo-Bighash
- Education
- 21 July 2020
TLDR
Explicit Constructions of Infinite Families of MSTD Sets
- S. Miller, Brooke Orosz, Daniel Scheinerman
- Mathematics
- 26 September 2008
One- and two-level densities for rational families of elliptic curves: evidence for the underlying group symmetries
- S. Miller
- MathematicsCompositio Mathematica
- 12 October 2003
Following Katz–Sarnak, Iwaniec–Luo–Sarnak and Rubinstein, we use the one- and two-level densities to study the distribution of low-lying zeros for one-parameter rational families of elliptic curves…
A Derivation of the Pythagorean Won-Loss Formula in Baseball
- S. Miller
- Mathematics
- 29 September 2005
It has been noted that in many professional sports leagues a good predictor of a team’s end of season won-loss percentage is Bill James’ Pythagorean Formula RSobs γ RSobs +RAobs γ , where RSobs…
A Symplectic Test of the L-Functions Ratios Conjecture
- S. Miller
- Mathematics
- 6 April 2007
Recently Conrey, Farmer and Zirnbauer [8, 9] conjectured formulas for the averages over a family of ratios of products of shifted L-functions. Their L-functions Ratios Conjecture predicts both the…
Benford’s Law Applied to Hydrology Data—Results and Relevance to Other Geophysical Data
- M. Nigrini, S. Miller
- Environmental Science
- 29 August 2007
Abstract
Benford’s Law gives the expected frequencies of the digits in tabulated data and asserts that the lower digits (1, 2, and 3) are expected to occur more frequently than the higher digits.…
Introduction to: 1- and 2-Level Densities for Families of Elliptic Curves: Evidence for the Underlying Group Symmetries
- S. Miller
- Mathematics
- 2003
Following Rubinstein [Ru], Iwaniec-Luo-Sarnak [ILS], and Katz-Sarnak [KS1], [KS2], we use the 1and 2-level densities to study the distribution of low lying zeros for families of elliptic curves. For…
When almost all sets are difference dominated
- P. Hegarty, S. Miller
- MathematicsRandom Struct. Algorithms
- 23 July 2007
TLDR
The low lying zeros of a GL(4) and a GL(6) family of $L$-functions
We investigate the large weight ($k\to\infty$) limiting statistics for the low lying zeros of a GL(4) and a GL(6) family of $L$-functions, $\{L(s,\phi \times f): f \in H_k\}$ and $\{L(s,\phi \times…
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