Errata and Addenda to Mathematical Constants

Abstract

We humbly and briefly offer corrections and supplements to Mathematical Constants (2003) and Mathematical Constants II (2019), both published by Cambridge University Press. Comments are always welcome.

arXiv comment168 pages

References in corpus (180)

• A fast Monte Carlo algorithm for site or bond percolation
• Efficient Monte Carlo algorithm and high-precision results for percolation
• New upper bounds on sphere packings I
• The sphere packing problem in dimension 24
• The sphere packing problem in dimension 8
• Group-theoretic algorithms for matrix multiplication
• Euler's constant: Euler's work and modern developments
• The number of matchings in random graphs
• Typical random 3-SAT formulae and the satisfiability threshold
• An introduction to the dimer model
• Random Convex Hulls and Extreme Value Statistics
• Dense crystalline dimer packings of regular tetrahedra
• Bootstrap percolation in three dimensions
• On the absolute constants in the Berry-Esseen type inequalities for identically distributed summands
• The ternary Goldbach conjecture is true
• A parallel algorithm for the enumeration of self-avoiding polygons on the square lattice
• The enumeration of simple permutations
• A new transfer-matrix algorithm for exact enumerations: Self-avoiding polygons on the square lattice
• Exact Asymptotic Results for a Model of Sequence Alignment
• Unified Solution of the Expected Maximum of a Random Walk and the Discrete Flux to a Spherical Trap
• Sequential cavity method for computing free energy and surface pressure
• Riemann Zeta Function
• Pseudorandom Number Generators and the Square Site Percolation Threshold
• The generalized-Euler-constant function $\gamma (z)$ and a generalization of Somos's quadratic recurrence constant
• On partitions avoiding 3-crossings
• Limiting distributions for additive functionals on Catalan trees
• Fractal analysis for sets of non-differentiability of Minkowski's question mark function
• Rounding of continuous random variables and oscillatory asymptotics
• Square lattice Ising model susceptibility: connection matrices and singular behavior of ${\chi }^{(3)}$ and ${\chi }^{(4)}$
• New lower bounds for the number of $(\le k)$-edges and the rectilinear crossing number of $K_n$
• Rigorous effective bounds on the Hausdorff dimension of continued fraction Cantor sets: a hundred decimal digits for the dimension of $E_2$
• Some Exact Results for Spanning Trees on Lattices
• Simulation of percolation on massively-parallel computers
• Random trimer tilings
• The density of rational points on Cayley's cubic surface
• On the Generalized Poisson Distribution
• Monomer-dimer model in two-dimensional rectangular lattices with fixed dimer density
• Packing dimers on $(2p+1)\times (2q+1)$ lattices
• Complementary algorithms for graphs and percolation
• Rigorous confidence intervals for critical probabilities
• The high-temperature expansions of the higher susceptibilities for the Ising model in general dimension d
• New estimates of the convergence rate in the Lyapunov theorem
• The Pfaffian solution of a dimer-monomer problem: Single monomer on the boundary
• On gamma quotients and infinite products
• Upper bound on the packing density of regular tetrahedra and octahedra
• Yang-Lee edge singularities from extended activity expansions of the dimer density for bipartite lattices of dimensionality 2 <= d <= 7
• Euler's constant, q-logarithms, and formulas of Ramanujan and Gosper
• Three-loop electroweak corrections to the W-boson mass and sin^2 theta_eff in the large Higgs mass limit
• Random Distances Associated with Hexagons
• On the minimal travel time needed to collect n items on a circle
• Approximating the monomer-dimer constants through matrix permanent
• The Grothendieck constant is strictly smaller than Krivine's bound
• Sampling the Lindelöf Hypothesis with the Cauchy Random Walk
• Improved bounds on the number of ternary square-free words
• The Minkowski question mark function: explicit series for the dyadic period function and moments
• Random Distances Associated with Rhombuses
• Counting numbers in multiplicative sets: Landau versus Ramanujan
• On the average number of elements in a finite field with order or index in a prescribed residue class
• New series representation for Madelung constant
• Renyi's Parking Problem Revisited
• Markov's Transformation of Series and the WZ Method
• On the probability distribution of the gcd and lcm of $r$-tuples of integers
• Mertens' Proof of Mertens' Theorem
• Validations of the Asymptotic Matching Conjectures
• The maximal order of Stern's diatomic sequence
• Higher order expansions for the entropy of a dimer or a monomer-dimer system on d-dimensional lattices
• A densest compact planar packing with two sizes of discs
• A few equalities involving integrals of the logarithm of the Riemann zeta-function and equivalent to the Riemann hypothesis II
• Infinite products with strongly $B$-multiplicative exponents
• Point sets that minimize $(\le k)$-edges, 3-decomposable drawings, and the rectilinear crossing number of $K_{30}$
• Improved lower bounds on book crossing numbers of complete graphs
• Random Distances Associated With Equilateral Triangles
• C^m Eigenfunctions of Perron-Frobenius Operators and a New Approach to Numerical Computation of Hausdorff Dimension
• Series of Reciprocal Powers of k-almost Primes
• Pairwise Relative Primality of Positive Integers
• The $r$th moment of the divisor function: an elementary approach
• Lower Bound for Convex Hull Area and Universal Cover Problems
• The difference between two Stieltjes constants
• Random chords and point distances in regular polygons
• On Linnik's constant
• Searching for a Shoreline
• On linear forms containing the Euler constant
• Mean Width of a Regular Simplex
• The univalent Bloch-Landau constant, harmonic symmetry and conformal glueing
• Two algorithms for evaluation of the Newman digit sum, and a new proof of Coquet's theorem
• An Explicit Formula Relating Stieltjes Constants and Li's Numbers
• The number of cycles of specified normalized length in permutations
• Exact Results for Average Cluster Numbers in Bond Percolation on Lattice Strips
• The cycle structure of compositions of random involutions
• Random Distances Associated with Arbitrary Triangles: A Systematic Approach between Two Random Points
• On the generation of Heronian triangles
• Generalising the Hardy-Littlewood Method for Primes
• Planar triangulations with real chromatic roots arbitrarily close to four
• Transfer operator for the Gauss' continued fraction map. I. Structure of the eigenvalues and trace formulas
• On a continued fraction expansion for Euler's constant
• On the regular sum-free sets
• The 2-page crossing number of $K_n$
• The distribution function of the distance between two random points in a right-angled triangle
• On the expected number of zeros of nonlinear equations
• Replica Symmetry and Combinatorial Optimization
• Rigorous Confidence Intervals on Critical Thresholds in 3 Dimensions
• On the Limiting Distribution for the Longest Alternating Sequence in a Random Permutation
• An elementary proof of uniqueness of Markoff numbers which are prime powers
• Improved upper bounds in the moving sofa problem
• Random Distances Associated with Trapezoids
• Lower bounds for the simplexity of the n-cube
• Turan's problem 10 revisited
• Schanuel's conjecture and algebraic powers z^w and w^z with z and w transcendental
• The Integral of the Riemann xi-function
• The asymptotics of group Russian roulette
• A few equalities involving integrals of the logarithm of the Riemann zeta-function and equivalent to the Riemann hypothesis III. Exponential weight functions
• On the Reinhardt Conjecture
• The Enumeration of Prudent Polygons by Area and its Unusual Asymptotics
• Odd Entries in Pascal's Trinomial Triangle
• Two-Dimensional Analogs of the Minkowski ?(x) Function
• Primes in intervals of bounded length
• Idempotents and Nilpotents Modulo n
• A Hypergeometric Approach, Via Linear Forms Involving Logarithms, to Irrationality Criteria for Euler's Constant
• Feynman's sunshine numbers
• Newman's conjecture in various settings
• Increasing and Decreasing Subsequences of Permutations and Their Variants
• On $k$-noncrossing partitions
• Pairwise non-coprimality of triples
• An improved lower bound for finite additive 2-bases
• Elastic energy of a convex body
• Results and conjectures related to a conjecture of Erdős concerning primitive sequences
• The Jamming Constant of Uniform Random Graphs
• On the derivative of the Minkowski question mark function $?(x)$
• A lower bound on opaque sets
• Resolving Conflicts and Electing Leaders
• Simplifications of the Keiper/Li approach to the Riemann Hypothesis
• A Variation on Mills-Like Prime-Representing Functions
• Hardy-Littlewood Constants Embedded into Infinite Products over All Positive Integers
• Arithmetic of Catalan's constant and its relatives
• On the number of pairs of positive integers $x,y\le H$ such that $x^2+y^2+1$ is squarefree
• A note on the real part of the Riemann zeta-function
• The regularized product of the Fibonacci numbers
• On the Hermite problem for cubic irrationalities
• Typical Dispersion and Generalized Lyapunov Exponents
• Proof of the Conjecture that the Planar Self-Avoiding Walk has Root Mean Square Displacement Exponent 3/4
• Square-free values of $n^2+1$
• Formula for the Mean Square Displacement Exponent of the Self-Avoiding Walk in 3, 4 and All Dimensions
• When only the last one will do
• An Improved Lower Bound for Moser's Worm Problem
• On $(\le k)$-edges, crossings, and halving lines of geometric drawings of $K_n$
• The prime analog of the Kepler-Bouwkamp constant
• On computable approximations of Landau's constant
• A Generalization of Gauss-Kuzmin-Lévy Theorem
• Wright's Fourth Prime
• The variance of the Euler totient function
• Tightly Circumscribed Regular Polygons
• Delange's Tauberian theorem and asymptotic normality of random ordered factorizations of integers
• Twenty Digits of Some Integrals of the Prime Zeta Function
• Mean value one of prime-pair constants
• A Proof on Hypothesis of Dirichlet Divisor Problem
• A slight improvement to Korenblum's constant
• Some bounds and limits in the theory of Riemann's zeta function
• A New Slant on Lebesgue's Universal Covering Problem
• A note on the number of abelian groups of a given order
• A product representation of pi
• 3--symmetric and 3--decomposable drawings of $K_n$ (extended version)
• On the mean square of the error term for the two-dimensional divisor problems(II)
• Large gaps between consecutive maxima of the Riemann zeta-function on the critical line
• Numerical Evaluation Of the Oscillatory Integral over exp(i*pi*x)*x^(1/x) between 1 and infinity
• On the Probability of Relative Primality in the Gaussian Integers
• Longest common subsequences and the Bernoulli matching model: numerical work and analyses of the r-reach simplification
• Mean Values of the Logarithmic Derivative of the zeta Function and the GUE Hypothesis
• Summation of rational series twisted by strongly B-multiplicative coefficients
• The Reinhardt Conjecture as an Optimal Control Problem
• A Generalization of the Gauss-Kuzmin-Wirsing constant
• A Cameron and Erdös conjecture on counting primitive sets
• On a Detail in Hales's "Dense Sphere Packings: A Blueprint for Formal Proofs"
• Univalence criteria and analogs of the John constant
• Sums of three squareful numbers
• Polynomials with integer coefficients and their zeros
• A note on products involving zeta(3) and Catalan's constant
• More Infinite Products: Thue-Morse and the Gamma function
• Where do the maximum absolute $q$-series coefficients of $(1-q)(1-q^2)(1-q^3)\dots (1-q^{n-1})(1-q^n)$ occur?
• A proof of the Conjecture of Lehmer
• Diophantine problems related to the Omega constant