Table of Contents
16 relations: Analytic function, Complex analysis, Complex number, Fourier series, Functional equation, Group action, Hecke algebra, Hecke operator, Mathematics, Modular arithmetic, Modular form, Modular group, Number theory, P-adic modular form, Ramanujan tau function, Upper half-plane.
Analytic function
In mathematics, an analytic function is a function that is locally given by a convergent power series.
See Modular forms modulo p and Analytic function
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.
See Modular forms modulo p and Complex analysis
Complex number
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted, called the imaginary unit and satisfying the equation i^.
See Modular forms modulo p and Complex number
Fourier series
A Fourier series is an expansion of a periodic function into a sum of trigonometric functions.
See Modular forms modulo p and Fourier series
Functional equation
In mathematics, a functional equation is, in the broadest meaning, an equation in which one or several functions appear as unknowns.
See Modular forms modulo p and Functional equation
Group action
In mathematics, many sets of transformations form a group under function composition; for example, the rotations around a point in the plane.
See Modular forms modulo p and Group action
Hecke algebra
In mathematics, the Hecke algebra is the algebra generated by Hecke operators, which are named after Erich Hecke. Modular forms modulo p and Hecke algebra are modular forms.
See Modular forms modulo p and Hecke algebra
Hecke operator
In mathematics, in particular in the theory of modular forms, a Hecke operator, studied by, is a certain kind of "averaging" operator that plays a significant role in the structure of vector spaces of modular forms and more general automorphic representations. Modular forms modulo p and Hecke operator are modular forms.
See Modular forms modulo p and Hecke operator
Mathematics
Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.
See Modular forms modulo p and Mathematics
Modular arithmetic
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus.
See Modular forms modulo p and Modular arithmetic
Modular form
In mathematics, a modular form is a (complex) analytic function on the upper half-plane, \,\mathcal\,, that satisfies. Modular forms modulo p and modular form are modular forms.
See Modular forms modulo p and Modular form
Modular group
In mathematics, the modular group is the projective special linear group \operatorname(2,\mathbb Z) of matrices with integer coefficients and determinant 1. Modular forms modulo p and modular group are modular forms.
See Modular forms modulo p and Modular group
Number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions.
See Modular forms modulo p and Number theory
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. Modular forms modulo p and p-adic modular form are modular forms.
See Modular forms modulo p and P-adic modular form
Ramanujan tau function
The Ramanujan tau function, studied by, is the function \tau: \mathbb \rarr\mathbb defined by the following identity: where with, \phi is the Euler function, is the Dedekind eta function, and the function is a holomorphic cusp form of weight 12 and level 1, known as the discriminant modular form (some authors, notably Apostol, write \Delta/(2\pi)^ instead of \Delta). Modular forms modulo p and Ramanujan tau function are modular forms.
See Modular forms modulo p and Ramanujan tau function
Upper half-plane
In mathematics, the upper half-plane, is the set of points in the Cartesian plane with The lower half-plane is the set of points with. Modular forms modulo p and upper half-plane are modular forms.
See Modular forms modulo p and Upper half-plane