What is the modular form used for?

For example, modular forms are central to the proof of Fermat’s Last Theorem, and can be used to show other Diophantine results, such as the fact that 144 is the largest Fibonacci number which is also a perfect power.

Why are modular forms called modular?

Technically, if the weight is k, then it’s a differential k-form on the folded space. This is where the name comes from. The folded space is a modular curve, and the function is a differential form. Hence: modular form.

Who discovered modular function?

M is called the sum of the numbers modulo N. Using notation introduced by the German mathematician Carl Friedrich Gauss in 1801, one writes, for example, 2 + 4 + 3 + 7 ≡ 6 (mod 10), where the symbol ≡ is read “is congruent to.” We have a number of things, but we do not know exactly how many.

What does it mean for an elliptic curve to be modular?

A modular elliptic curve is an elliptic curve E that admits a parametrisation X0(N) → E by a modular curve. The modularity theorem, also known as the Taniyama–Shimura conjecture, asserts that every elliptic curve defined over the rational numbers is modular.

What is modular design architecture?

Modular architecture has been introduced as a concept which involves assembling multiple pre-fabricated modules on site to create a working unit. By joining similar elements together in various ways, modular architecture allows for more flexibilities in design and standardized repair.

Who proved the Taniyama Shimura conjecture?

Six years later Christophe Breuil, Brian Conrad, Fred Diamond, and Richard Taylor have finally announced a proof of the full Shimura- Taniyama-Weil conjecture for all elliptic curves over Q.

What is J function?

The J-function, which synthesizes the fluid IFT, wettability, permeability, and porosity, is used to represent the characteristics of the reservoir capillary pressure curve. Therefore, the J-function can be used to represent the capillary pressure curve of a reservoir.

Who proved the epsilon conjecture?

Ribet
The conjecture that Frey’s elliptic curve was not modular. The conjecture was quickly proved by Ribet (Ribet’s theorem) in 1986, and was an important step in the proof of Fermat’s last theorem from the Taniyama-Shimura conjecture.

When were modular forms invented?

The first modular forms (of level 4, not level 1) were found by Gauss in his work on the arithmetic-geometric mean around 1800, and it would take until the end of the 19th century for the term “modular form” to be introduced, in 1890.

How does MOD function work?

The MOD function returns the remainder after division. For example, MOD(3,2) returns 1, because 2 goes into 3 once, with a remainder of 1. The MOD function takes two arguments: number and divisor. Number is the number to be divided, and divisor is the number used to divide.

Why are elliptic curves important?

1) Elliptic Curves provide security equivalent to classical systems (like RSA), but uses fewer bits. 2) Implementation of elliptic curves in cryptography requires smaller chip size, less power consumption, increase in speed, etc.

What is modular design write down its advantages?

Modular software design is done by breaking the larger code into smaller sections, think modules, that hold specific functions. Modular design is shown to improve the design process by allowing better re-usability, workload handling, and easier debugging processes.