Is there an immediate proof not using Minkowski's bound that we have $|\Delta_K|>1$ for all number fields $K \ne \mathbb Q$?
2026-03-24 19:08:58.1774379338
Why is the discriminant of number fields greater 1?
281 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in ALGEBRAIC-NUMBER-THEORY
- Splitting of a prime in a number field
- algebraic integers of $x^4 -10x^2 +1$
- Writing fractions in number fields with coprime numerator and denominator
- Tensor product commutes with infinite products
- Introduction to jacobi modular forms
- Inclusions in tensor products
- Find the degree of the algebraic numbers
- Exercise 15.10 in Cox's Book (first part)
- Direct product and absolut norm
- Splitting of primes in a Galois extension
Related Questions in DISCRIMINANT
- discriminant and irreducibility of $x^p - (p+1)x - 1$
- Discriminant of $X^n+pX+q$
- How to solve $ax^x+bx+c=0$?
- galois group of irreducible monic cubic polynomial
- discriminant as a product of pairwise differences of roots
- Irreducibility of $x^3-6x-2$ in $Q[x]$
- Find the points that are closest and farthest from $(0,0)$ on the curve $3x^2-2xy+2y^2=5$
- Find k for Positive Definite Quadratic Form
- Minimize objective function for least square classification
- Quadratic Equations(determine the nature of roots)
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
There is a proof by E. Landau in 1922 using the pigeonhole principle.
There is an English translation.