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Что (кто) такое P-adic modular form - определение
P-adic modular form
In mathematics, a p-adic modular form is a p-adic analog of a modular form, with coefficients that are p-adic numbers rather than complex numbers. introduced p-adic modular forms as limits of ordinary modular forms, and shortly afterwards gave a geometric and more general definition.
Modular form
ANALYTIC FUNCTION ON THE UPPER HALF-PLANE WITH A CERTAIN BEHAVIOR UNDER THE MODULAR GROUP
Modular forms; Elliptic modular form; Modular function; Level of a modular form; Weight of a modular form; Nebentypus character; Nebentype character; Q-expansion; Modular form and modular function; Modular function and modular form
In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition. The theory of modular forms therefore belongs to complex analysis but the main importance of the theory has traditionally been in its connections with number theory.
P-adic L-function
In mathematics, a p-adic zeta function, or more generally a p-adic L-function, is a function analogous to the Riemann zeta function, or more general L-functions, but whose domain and target are p-adic (where p is a prime number). For example, the domain could be the p-adic integers Zp, a profinite p-group, or a p-adic family of Galois representations, and the image could be the p-adic numbers Qp or its algebraic closure.
