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Distribution of Eigenvalues for the Ensemble of Real Symmetric Toeplitz Matrices
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.…
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Explicit Constructions of Infinite Families of MSTD Sets
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An Invitation to Modern Number Theory
TLDR
This website is an invitation to modern number theory that will be your best choice for better reading book and you can take the book as a source to make better concept.
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Investigations of Zeros near the Central Point of Elliptic Curve L-Functions
TLDR
The effects of zeros at the central point on nearby zeros of elliptic-curve L-functions, especially for one-parameter families of rank r over ℚ are explored, and it is conjecture that the r family zeros do not repel in the limit.
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A Derivation of the Pythagorean Won-Loss Formula in Baseball
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…
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One- and two-level densities for rational families of elliptic curves: evidence for the underlying group symmetries
  • S. Miller
  • Mathematics
    Compositio 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…
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Introduction to: 1- and 2-Level Densities for Families of Elliptic Curves: Evidence for the Underlying Group Symmetries
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…
A Symplectic Test of the L-Functions Ratios Conjecture
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…
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Benford’s Law Applied to Hydrology Data—Results and Relevance to Other Geophysical Data
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.…
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The Distribution of the Largest Nontrivial Eigenvalues in Families of Random Regular Graphs
TLDR
These graphs have important applications in communication network theory, allowing the construction of superconcentrators and nonblocking networks, as well as in coding theory and cryptography, and are well modeled by the β = 1 Tracy-Widom distribution for several families.
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