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Deligne's Conjecture (L-functions)
In mathematics, the study of special values of -functions is a subfield of number theory devoted to generalising formulae such as the Leibniz formula for pi, Leibniz formula for , namely 1 \,-\, \frac \,+\, \frac \,-\, \frac \,+\, \frac \,-\, \cdots \;=\; \frac,\! by the recognition that expression on the left-hand side is also L(1) where L(s) is the Dirichlet L-function, Dirichlet -function for the field of Gaussian rational numbers. This formula is a special case of the analytic class number formula, and in those terms reads that the Gaussian field has class number problem, class number 1. The factor \tfrac14 on the right hand side of the formula corresponds to the fact that this field contains four roots of unity. Conjectures There are two families of conjectures, formulated for general classes of L-function, -functions (the very general setting being for -functions associated to Chow motives over number fields), the division into two reflecting the questions of: how to repl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
