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The Heath-Brown-Moroz constant is defined by C_(Heath-Brown-Moroz) = product_(p)(1-1/p)^7(1+(7p+1)/(p^2)) (1) = 0.00131764115... (2) (OEIS A118228), where the product is ...

Let alpha_i and A_i be algebraic numbers such that the A_is differ from zero and the alpha_is differ from each other. Then the expression ...

For any two nonzero p-adic numbers a and b, the Hilbert symbol is defined as (a,b)={1 if z^2=ax^2+by^2 has a nonzero solution; -1 otherwise. (1) If the p-adic field is not ...

The Hodge conjecture asserts that, for particularly nice types of spaces called projective algebraic varieties, the pieces called Hodge cycles are actually rational linear ...

A relation expressing a sum potentially involving binomial coefficients, factorials, rational functions, and power functions in terms of a simple result. Thanks to results by ...

A hypergeometric series sum_(k)c_k is a series for which c_0=1 and the ratio of consecutive terms is a rational function of the summation index k, i.e., one for which ...

If an integrable quasiperiodic system is slightly perturbed so that it becomes nonintegrable, only a finite number of n-map cycles remain as a result of mode locking. One ...

A law is a mathematical statement which always holds true. Whereas "laws" in physics are generally experimental observations backed up by theoretical underpinning, laws in ...

A procedure for determining the behavior of an nth order ordinary differential equation at a removable singularity without actually solving the equation. Consider ...

The series for the inverse tangent, tan^(-1)x=x-1/3x^3+1/5x^5+.... Plugging in x=1 gives Gregory's formula 1/4pi=1-1/3+1/5-1/7+1/9-.... This series is intimately connected ...