# 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

**3**

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### If a and b are roots of polynomials P and Q, then what polynomials are a+b and ab a roots of? [on hold]

**4**

**5**answers

### Connection Between Knot Theory and Number Theory

**6**

**0**answers

### Extension of Erdos-Selfridge Theorem

**10**

**1**answer

### Is there an elementary proof that there are infinitely many primes that are *not* completely split in an abelian extension?

**4**

**0**answers

### Does the Gauss sum attached to $\chi$ ever belong to $\mathbb{Q}(\chi)$?

**1**

**1**answer

### Bound on number of proper ideals of norm equal to n

**4**

**0**answers

### Hodge-Tate weights of cohomological cuspidal automorphic representation

**4**

**1**answer

### Why do polynomials $x^n + 1 \bmod N$ close a shorter cycle when $n$ is even than when $n$ is odd?

**0**

**0**answers

### Absolute convergence of the Fourier series of a smooth adelic function

**37**

**1**answer

### Class field theory - a “dead end”?

**4**

**0**answers

### Computation of Hochschild homology

**4**

**1**answer

### Confusion about topological Hochschild homology and $\mathbb{Z}_p$-topological Hochschild homology

**6**

**1**answer

### The Hilbert symbols of quaternion algebras over a totally real field

**9**

**0**answers

### How small may the discriminant of an $S_d$-field be?

**5**

**0**answers