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In mathematics, a character sum is a sum () of values of a Dirichlet character χ modulo N, taken over a given range of values of n.Such sums are basic in a number of questions, for example in the distribution of quadratic residues, and in particular in the classical question of finding an upper bound for the least quadratic non-residue modulo N.
In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
Denotes the sum of a finite number of terms, which are determined by subscripts and superscripts (which can also be placed below and above), such as in = or < < <. 2. Denotes a series and, if the series is convergent , the sum of the series .
The Unicode Standard encodes almost all standard characters used in mathematics. [1] Unicode Technical Report #25 provides comprehensive information about the character repertoire, their properties, and guidelines for implementation. [1] Mathematical operators and symbols are in multiple Unicode blocks. Some of these blocks are dedicated to, or ...
Grouped by their numerical property as used in a text, Unicode has four values for Numeric Type. First there is the "not a number" type. Then there are decimal-radix numbers, commonly used in Western style decimals (plain 0–9), there are numbers that are not part of a decimal system such as Roman numbers, and decimal numbers in typographic context, such as encircled numbers.
There is another kind of character reference called a character entity reference, which allows a character to be referred to by a name instead of a number. (Naming a character creates a character entity.) HTML defines some character entities, but not many; all other characters can only be included by direct encoding or using NCRs.
The nnnn or hhhh may be any number of digits and may include leading zeros. The hhhh may mix uppercase and lowercase, though uppercase is the usual style. In contrast, a character entity reference refers to a character by the name of an entity which has the desired character as its replacement text.
In mathematics, a Jacobi sum is a type of character sum formed with Dirichlet characters. Simple examples would be Jacobi sums J ( χ , ψ ) for Dirichlet characters χ , ψ modulo a prime number p , defined by