Complex number refers to the number a+bi which can be written in the following form, where A and B are real numbers and I is imaginary unit (i.e.-1 root). It was first put forward by Italian Milan scholar Cardan in the16th century, and this concept was gradually accepted by mathematicians through the work of D'Alembert, De Moivre, Euler and Gauss. There are many representations of complex numbers, such as vector representation, triangle representation and exponential representation. It meets the following requirements.

Trigonometric function is a kind of transcendental function in elementary function in mathematics. Their essence is the mapping between the set of arbitrary angles and a set of ratio variables. Trigonometric function is usually defined in plane rectangular coordinate system, and its domain is the whole real number domain. The other is defined in a right triangle, but it is incomplete. Modern mathematics describes them as the limits of infinite series and the solutions of differential equations. Its definition extends to the complex number system. It contains six basic functions: sine, cosine, tangent, cotangent, secant and cotangent. Because of its periodicity, trigonometric function has no inverse function in the sense of single-valued function. Trigonometric functions have more important applications in complex numbers. Trigonometric function is also a common tool in physics. Generally speaking, for the mathematical object X, we can define the complex number column {\λ_ X}. } _ {n = 1} The two are closely related. According to P.R.Langlands conjecture, generally speaking, all meaningful L- functions come from automorphism L- functions. Arithmetic L- function: In short, it is an L- function with arithmetic meaning, such as Riemann ζ-function, Dirichlet L- function, Dai Dejin ζ-function, Haas-Weil L- function of elliptic curve, Atin L- function, etc. Automorphic L- functions: all.