# Questions tagged [algebraic-number-theory]

Algebraic number fields, Algebraic integers, Arithmetic Geometry, Elliptic Curves, Function fields, Local fields, Arithmetic groups, Automorphic forms, zeta functions, $L$-functions, Quadratic forms, Quaternion algebras, Homogenous forms, Class groups, Units, Galois theory, Group cohomology, Étale cohomology, Motives, Class field theory, Iwasawa theory, Modular curves, Shimura varieties, Jacobian varieties, Moduli spaces

**4**

**1**answer

### Deformations of the Riemann zeta function

**0**

**0**answers

### Image of extension ideal classes homomorphism in ideal class group under Artin map in class field theory

**11**

**2**answers

### Conceptual explanations of the class numbers for the first few $\mathbb{Q}(\sqrt{p})$ with odd conductor

**0**

**0**answers

### Image of Frobenius element under irreducible representation is diagonalizable

**4**

**0**answers

### Discriminant mod 8

**0**

**0**answers

### Status of the $n$ conjecture, and as a reference request what about ideas or techniques that could be potentially interesting

**4**

**0**answers

### Maximal $\mathbb{Q}$-split torus in center of Weil restriction of $\text{GL}_n$ over a number ring

**1**

**1**answer

### Theory of extensions of non-archimedian local fields

**1**

**1**answer

### Looking for a paper by Landau and one by Watson

**0**

**0**answers

### Distribution of prime ideals by norm

**4**

**1**answer

### How is class of composition of two quadratic fields is related class numbers of quadratic field?

**0**

**1**answer

### On $L$-function of permutation representation

**0**

**0**answers

### On Prime Numbers which can be Norms of an Integral Ideal of a Number Field

**1**

**0**answers

### Small pants in arithmetic hyperbolic surfaces of high degree

**0**

**1**answer

### Logarithms of $L$-functions of irreducible characters of Galois group

**3**

**1**answer

### Level vs. conductor of a supercuspidal representation

**2**

**1**answer

### Existence of analytic continuation of Dirichlet series corresponding to the indicator sequence of a complement of a special multiplicative set

**1**

**1**answer

### The existence of rational points [closed]

**13**

**0**answers

### Galois groups of special polynomials

**3**

**1**answer

### English reference for the Brauer-Kuroda formula

**1**

**2**answers

### Methods of sheaf theory for solving Diophantine equations

**2**

**0**answers

### Studying the vast world of Number Theory [closed]

**2**

**1**answer

### Extension of Dedekind domains and their codifferent

**19**

**2**answers

### Number of real roots of irreducible polynomials that are solvable by radicals

**2**

**0**answers

### Where is the flaw in this argument with $p$-adic extensions?

**6**

**0**answers

### Coherent cohomology of the generic fiber of Lubin-Tate space vs. of Lubin-Tate space considered rationally?

**2**

**2**answers

### Natural number solutions for equations of the form $\frac{a^2}{a^2-1} \cdot \frac{b^2}{b^2-1} = \frac{c^2}{c^2-1}$

**4**

**1**answer

### Do number rings tend to Z?

**2**

**0**answers

### Compatible systems of $l$-adic Galois representations as sheaves

**0**

**0**answers

### properties of anti-cyclotomic extension

**1**

**0**answers

### self dual character of local fields and global fields

**6**

**1**answer

### When are all signatures represented by units?

**1**

**0**answers

### Regulator of number fields of a special form

**7**

**0**answers

### Cohn's eight diophantine equations

**0**

**0**answers

### Commensurability of arithmetic, irreducible, nonuniform lattices

**1**

**0**answers

### A structure on the groupoid of algebraic closures

**1**

**0**answers

### $n$-variable polynomials modulo $p$

**8**

**2**answers

### Irrationality measure of arctan(1/3)

**3**

**0**answers

### How does Langlands define Artin L-functions?

**2**

**0**answers

### Does Langlands use the geometric Frobenius or the classical Frobenius in his papers?

**4**

**1**answer

### Which $p$-adic valuations of Weil numbers (that is, eigenvalues of Frobenius) are possible?

**1**

**1**answer

### Factoring cyclotomic polynomials over quadratic subfield

**3**

**1**answer

### Siegel's bad character

**2**

**0**answers

### The definition of Langlands' L-function $L(s,\pi,r)$ in the case of $\operatorname{GL}_1$

**9**

**3**answers

### Does the expression $x^4 +y^4$ take on all values in $\mathbb{Z}/p\mathbb{Z}$?

**1**

**0**answers

### Computing the kernel of some Artin-Map

**7**

**1**answer

### Finding $Q(\sqrt{-2})$-rational points on $X_0(33)$

**1**

**0**answers

### Transcendance in function fields

**5**

**1**answer

### A problem about real quadratic field

**3**

**0**answers