# Experimental Mathematics

## Volume 15 (2006)

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### Volume 15, Issue 1

"Fractals and Eigenvalues of the Laplacian on Certain Noncompact Surfaces

**Arthur Baragar**

The Probability that a Random Monic p-Adic Polynomial Splits

**Joe Buhler, Daniel Goldstein, David Moews, and Joel Rosenberg**

Random Matrix Theory and the Fourier Coefficients of Half-Integral Weight Forms

**J. Brian Conrey, Jon P. Keating, Michael Rubinstein, and Nina C. Snaith**

Topology of Plane Sections of Periodic Polyhedra with an Application to the Truncated Octahedron

**Roberto De Leo
Appendix**

On the Computation of Clebsch-Gordan Coefficients and the Dilation Effect

**Jesús A. De Loera and Tyrrell B. McAllister**

Diophantine Equations over Global Function Fields II: R-Integral Solutions of Thue Equations

**István Gaál and Michael Pohst**

A New Method to Obtain Series for 1/π and 1/π^{2}

**Jesús Guillera**

Drawing Bers Embeddings of the Teichmüller Space of Once-Punctured Tori

**Yohei Komori, Toshiyuki Sugawa, Masaaki Wada, and Yashusi Yamashita**

Nonlinear Elliptic Partial Difference Equations on Graphs

**John M. Neuberger**

Determination of the Best Constant in an Inequality of Hardy, Littlewood, and Polya

**T. C. Peachey and C. M. Enticott**

OPTi’s Algorithm for Discreteness Determination

**Masaaki Wada**

### Volume 15, Issue 2

The Superpolynomial for Knot Homologies

**Nathan M. Dunfield, Sergei Gukov, and Jacob Rasmussen**

Obtuse Triangular Billiards I: Near the (2, 3, 6) Triangle

**Richard Evan Schwartz**

Searching for Large Elite Primes

**Tom Müller**

Disturbing the Dyson Conjecture (in a GOOD Way)

**Andrew V. Sills and Doron Zeilberger**

Fast Searching for Andrews-Curtis Trivializations

**R. Sean Bowman and Stephen B. McCaul**

Experimentation and Conjectures in the Real Schubert Calculus for Flag Manifolds

**Jim Ruffo, Yuval Sivan, Evgenia Soprunova, and Frank Sottile**

The Mathieu Group M12 and Its Pseudogroup Extension M13

**John H. Conway, Noam D. Elkies, and Jeremy L. Martin**

Complexity of 4-Manifolds

**Francesco Costantino**

Abundant Numbers and the Riemann Hypothesis

**Keith Briggs**

### Volume 15, Issue 3

Investigations of Zeros near the Central Point of Elliptic Curve L-functions

**Steven J. Miller, with an appendix Eduardo Dueñez**

Experimental Determination of Apéry-Like Identities for z(2n + 2)

**David H. Bailey, Jonathan M. Borwein, and David M. Bradley**

Computing Varieties of Representations of Hyperbolic 3-Manifolds into SL(4,R)

**Daryl Cooper, Darren Long, and Morwen Thistlethwaite**

New Conjectural Lower Bounds on the Optimal Density of Sphere Packings

**S. Torquato and F. H. Stillinger**

New Bounds for the Principal Dirichlet Eigenvalue of Planar Regions

**Pedro Antunes and Pedro Freitas**

Broken-Cycle-Free Subgraphs and the Log-Concavity Conjecture for Chromatic Polynomials

**P. H. Lundlow and K. Markström**

On the Distribution of Analytic v|III| Values on Quadratic Twists of Elliptic Curves

**Patricia L. Quattrini**

Supplementary Graphs

Combinatorial Random Walks on 3-Manifolds

**Markus Banagl**

### Volume 15, Issue 4

Artin’s Conjecture, Turing’s Method, and the Riemann Hypothesis

**Andrew R. Booker**

A Class of Conjectured Series Representations for 1/π

**Jesús Guillera**

Heuristics for the Brauer-Manin Obstruction for Curves

**Bjorn Poonen**

Modeling Snow Crystal Growth I: Rigorous Results for Packard’s Digital Snowflakes

**Janko Gravner and David Griffeath**

The Nucleus of the Free Alternative Algebra

**I. R. Hentzel and L. A. Peresi**

Prehomogeneous Spaces Associated with Nilpotent Orbits in Simple Real Lie Algebras E_{6(6)} and E_{6(-26)} and Their Relative Invariants

**Steven Glann Jackson and Alfred G. Noël**

On Simultaneous Arithmetic Progressions on Elliptic Curves

**Irene García-Selfa and José M. Tornero**

Supplement as PDF or text

Some Geometry and Combinatorics for the S-Invariant of Ternary Cubics

**P. M. H. Wilson**

Supplementary Appendix

Fold Maps from the Sphere to the Plane

**D. Hacon, C. Mendes de Jesus, and M. C. Romero Fuster**

Zeros of {-1, 0, 1} Power Series and Connectedness Loci for Self-Affine Sets

**Pablo Shmerkin and Boris Solomyak**

Supplementary Code