2
votes
1answer
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 ...
-3
votes
1answer
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 ...
2
votes
2answers
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 ...
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 ...
4
votes
2answers
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 ...
1
vote
0answers
123 views

Non-holomorphic L-functions

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 $$ ...
0
votes
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 ...
3
votes
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 ...
5
votes
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 ...
21
votes
1answer
1k views

Special values of L-functions as periods

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 ...