# Tagged Questions

236 views

### Reference request: Grothendieck´s period conjecture?

I would like to know if Grothendieck published something about this conjecture? Is there some book (or expository article) about this conjecture? Is there any connection between this conjecture and ...
341 views

### Is SOC known to imply the Grand Riemann Hypothesis? [closed]

I'm currently working on a conditional proof of the Grand Riemann Hypothesis, which is based on the assumption that every field automorphism of $\mathbb{C}$ that commutes with an element of the ...
404 views

### Summation of certain series

Suppose $f(n)$ is a periodic function with period $q$. Now from this paper we get that if $\displaystyle\sum_{n=1}^{q}f(n)=0$ then ...
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 ...
442 views

### Blueprint of L-functions and need for introducing them ( Hasse-Weil L-functions )

Dear All, This question may appear elementary to all the experts in number theory , but forgive me. I really wanted to know how did the $L$-functions came into existence, especially the Hasse-Weil ...
In some old notes, I found the following conjecture: Let $\mathbb T$ denote the unit circle and let $\chi:{\mathbb N} \to {\mathbb T}$ be fully multiplicative. Then the L-series $$... 0answers 243 views ### Automorphism group of algebraic function fields Let K be a finite field and let F/K be a function field. Is it possible to deduce the genus of F/K from the automorphism group of G=Aut(F/K)? Is it possible to do so if we know that |G| is ... 4answers 700 views ### Values of Dirichlet L-funcions at natural numbers I want to know about reference of formulas for$$ L(s,D)=\sum_{n=1}^\infty \left(\frac{D}{n}\right)\,n^{-s} $$for s a positive integer number and D a fundamental discriminant. For s=1 we have ... 1answer 587 views ### The Correlation of the Mobius Function and Dirichlet Characters. Let \chi be a Dirichlet character, and define \phi_\chi (n) so that it satisfies$$\sum_{n=1}^\infty \phi_\chi (n)n^{-s}=\frac{\zeta(s-1)}{L(s,\chi)}. In other words ...
If $M$ is a pure motive over $\mathbb{Q}$, one cas define its $L$-function $L(M,s)$ which conjecturaly is a meromorphic function over $\mathbb{C}$ with finitely many poles. For example, when ...