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There are at least two statements which go by the name of Artin's conjecture. If r is any complex finite-dimensional representation of the absolute Galois group of a number ...

A requirement necessary for a given statement or theorem to hold. Also called a criterion.

The scalar form of Laplace's equation is the partial differential equation del ^2psi=0, (1) where del ^2 is the Laplacian. Note that the operator del ^2 is commonly written ...

A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of ...

Let T_n(x) be an arbitrary trigonometric polynomial T_n(x)=1/2a_0+{sum_(k=1)^n[a_kcos(kx)+b_ksin(kx)]} (1) with real coefficients, let f be a function that is integrable over ...

First published in Riemann's groundbreaking 1859 paper (Riemann 1859), the Riemann hypothesis is a deep mathematical conjecture which states that the nontrivial Riemann zeta ...

A series is an infinite ordered set of terms combined together by the addition operator. The term "infinite series" is sometimes used to emphasize the fact that series ...

A loose term for a true statement which may be a postulate, theorem, etc.

If f(x,y) is an analytic function in a neighborhood of the point (x_0,y_0) (i.e., it can be expanded in a series of nonnegative integer powers of (x-x_0) and (y-y_0)), find a ...

A problem also known as the points problem or unfinished game. Consider a tournament involving k players playing the same game repetitively. Each game has a single winner, ...