In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group G to the complex numbers which is invariant under the action of a discrete subgroup \Gamma \subset G of the topological group.

What is an automorphic representation?

Automorphic representations

Inside an L² space for a quotient of the adelic form of G, an automorphic representation is a representation that is an infinite tensor product of representations of p-adic groups, with specific enveloping algebra representations for the infinite prime(s).

What is a modular form in math?

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.

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.

What is the function of modulus?

A modulus function is a function which gives the absolute value of a number or variable. It produces the magnitude of the number of variables. It is also termed as an absolute value function.

Kevin Buzzard (lecture 1/20) Automorphic Forms And The Langlands Program [2017]

36 related questions found

What is Automorphic number in C?

An Automorphic number is a number whose square ends with the same digits as the original number. E.g – 5, 6, 76 etc.

What is Automorphic number in Java?

A number is called an automorphic number if and only if the square of the given number ends with the same number itself. For example, 25, 76 are automorphic numbers because their square is 625 and 5776, respectively and the last two digits of the square represent the number itself.

What is meant by automorphic number?

An automorphic number is an integer whose square ends with the given integer, as (25)² = 625, and (76)² = 5776. Strobogrammatic numbers read the same after having been rotated through 180°; e.g., 69, 96, 1001.

How do you write an automorphic number Program?

Steps to Check Automorphic Number in Java

1. Input a number (num).
2. Square the number (sqr).
3. Count the number of digits of (num) using while loop (c).
4. Compare the last (c) digits of (sqr) with the (num).
5. If they are equal then the number is Automorphic else not.

Is 36 an automorphic number?

In mathematics, an automorphic number is a number whose square "ends" in the same digits as the number itself. For example, 5² = 25, 6² = 36, 76² = 5776, and 890625² = 793212890625, so 5, 6, 76 and 890625 are all automorphic numbers.

Is 5 an automorphic number?

An automorphic number is a number whose square ends with the number itself. For example, 5 is an automorphic number, 5*5 =25.

What is an Armstrong?

Armstrong number is a number that is equal to the sum of cubes of its digits. For example 0, 1, 153, 370, 371 and 407 are the Armstrong numbers.

What is Harshad number in Java?

A number is said to be the Harshad number if it is divisible by the sum of its digit. For example, if number is 156, then sum of its digit will be 1 + 5 + 6 = 12. Since 156 is divisible by 12. So, 156 is a Harshad number.

How do you find a narcissist number in Java?

Steps to Find Narcissistic Number

Count the number of digits of the given number N and store it in a variable power. Find the power of each digit and add the result in a variable sum. Compare the variable sum with the given number N. If both are equal, the given number is a narcissistic number, else not.

Is 18 a Harshad number?

The number 18 is a harshad number in base 10, because the sum of the digits 1 and 8 is 9 (1 + 8 = 9), and 18 is divisible by 9.

What is neon number in Java?

A positive integer whose sum of digits of its square is equal to the number itself is called a neon number.

Is Armstrong number and narcissistic number same?

In recreational number theory, a narcissistic number^[1][2] (also known as a pluperfect digital invariant (PPDI), an Armstrong number (after Michael F. Armstrong) or a plus perfect number) is a number that is the sum of its own digits each raised to the power of the number of digits.

What are narcissistic numbers in maths?

Thus, narcissistic numbers are numbers that can be represented by some kind of mathematical manipulation of their digits. A whole number, or integer, that is the sum of the nth powers of its digits (e.g., 153 = 1³ + 5³ + 3³) is called a perfect…

How do you find the Automorphic number in Python?

To check whether a number is automorphic or not:

1. Input a number.
2. Count the digits in the input number (n).
3. Compute the square of the number.
4. Extract the last 'n' digits from the square and check if it is same as the original number.
5. If so then the given number is Automorphic, otherwise not.

What is Krishnamurthy number in Java?

Krishnamurthy number is another special number in Java. A number is said to be Krishnamurthy if the factorial sum of all its digits is equal to that number. Krishnamurthy number is also referred to as a Strong number.

What is Armstrong number in Java?

Java Programming Java8Object Oriented Programming. An Armstrong number is a number which equals to the sum of the cubes of its individual digits. For example, 153 is an Armstrong number as − 153 = (1)3 + (5)3 + (3)3 153 1 + 125 + 27 154 153.

What is a tech number?

A number is called a tech number if the given number has an even number of digits and the number can be divided exactly into two parts from the middle. After equally dividing the number, sum up the numbers and find the square of the sum. ... For example, 3025 is a tech number.

How many 4 digit tech numbers are there?

Write a program to generate and print all four-digit tech numbers. = 3025 is a tech number.