4
votes
0answers
178 views

Do infinite and ramified local factors of the Dedekind zeta function of a tame number field characterize its local root numbers?

Let say you have two number fields, that are tamely ramified, and suppose that the $p$-part of their Dedekind zeta functions coincide for all prime $p$ which is ramified in either field. Suppose ...
2
votes
1answer
284 views

How do you calculate the Euler factors of the imprimitive symmetric square at primes with bad reduction?

The reference for this question is Coates and Schmidt, Iwasawa theory for the symmetric square. Let $G = \textrm{Gal}(\overline{\mathbb{Q}}/\mathbb{Q}))$ and let $D_r \supseteq I_r$ be a ...
19
votes
1answer
2k views

Iwasawa main conjectures vs Bloch-Kato conjectures

Let $p$ be a prime, $K$ be a number field, $S$ a finite set of finite places of $K$ containing the set $S_p$ of places above $p$ and the places at infinity, $G:=G_{K,S}$ the Galois group of the ...
13
votes
0answers
745 views

Special values of Artin L-functions

This question might be naive and might carry the heuristic that we are living in the best possible world a little too far. If so, I appreciate being told so. Background: Stark's conjecture interprets ...