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Results tagged with l-functions
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user 5015
Questions about generalizations of the Riemann Zeta function of arithmetic interest whose definition relies on meromorphic continuation of special kinds of Dirichlet series, such as Dirichlet L-functions, Artin L-functions, elements of the Selberg class, automorphic L-functions, Shimizu L-functions, p-adic L-functions, etc.
6
votes
Decomposition of Tate-Shafarevich groups in field extensions
There is the Stickelberg element $\Theta$ considered by Mazur and Tate which gives more information in this direction. It is conjectured to be in the Fitting ideal and hence in the annihilator of the …
- 8,945
13
votes
Does the number of roots of the modular form associated to an elliptic curve, on the positiv...
Let $Z$ be the number of zeroes of $y\mapsto f(iy)$ for $0<y<\infty$ and let $r$ be the analytic rank of $E$. Then $Z\geqslant r$ and $Z\equiv r \pmod{2}$ as I will explain below. I don't know of an e …
- 8,945
4
votes
Main conjecture for elliptic curves invariant under a $\mathbb{Q}$-isogeny
The full main conjecture is invariant under isogenies defined over $\mathbb{Q}$, not just the statement about $\mu$ and $\lambda$-invariants.
The only thing that changes on the analytic side is the …
- 8,945
5
votes
Accepted
Elliptic units and Euler system
Given that you have not seen cyclotomic units, I think you should start with them. Rubin's appendix to Lang's book(s) on cyclotomic fields is one place or the book by Coates and Sujatha. Then for elli …
- 8,945
2
votes
p-adic L-functions for (dual of) fine Selmer Groups
You leave out a bit of information, which I will fill in here; I hope correctly.
Let $E/\mathbb{Q}$ be an elliptic curve and let $\mathbb{Q}_{\infty}$ be the cyclotomic $\mathbb{Z}_p$-extension for a …
- 8,945