A \(p\)-adic Waldspurger formula
From MaRDI portal
Publication:2413076
DOI10.1215/00127094-2017-0045zbMath1444.11143arXiv1511.08172OpenAlexW3106238887MaRDI QIDQ2413076
Yifeng Liu, Wei Zhang, Shou-Wu Zhang
Publication date: 6 April 2018
Published in: Duke Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1511.08172
Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Arithmetic aspects of modular and Shimura varieties (11G18) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Results involving abelian varieties (11J95)
Related Items (17)
The Birch and Swinnerton-Dyer Conjecture: A brief survey ⋮ \(p\)-adic heights of generalized Heegner cycles ⋮ Power series expansions of modular forms and p-adic interpolation of the square roots of Rankin–Selberg special values ⋮ p-adic L-functions via local–global interpolation: the case of ⋮ Heegner cycles and congruences between anticyclotomic \(p\)-adic \(L\)-functions over CM-extensions ⋮ The congruent number problem and elliptic curves ⋮ A \(p\)-adic Waldspurger formula and the conjecture of Birch and Swinnerton-Dyer ⋮ GOLDFELD’S CONJECTURE AND CONGRUENCES BETWEEN HEEGNER POINTS ⋮ A unipotent circle action on 𝑝-adic modular forms ⋮ 2-Selmer groups, 2-class groups and rational points on elliptic curves ⋮ A proof of Perrin-Riou's Heegner point main conjecture ⋮ Anticyclotomic \(p\)-adic \(L\)-functions and Ichino's formula ⋮ On the non-vanishing of \(p\)-adic heights on CM abelian varieties, and the arithmetic of Katz \(p\)-adic \(L\)-functions ⋮ Horizontal non-vanishing of Heegner points and toric periods ⋮ On the non-triviality of the $p$-adic Abel–Jacobi image of generalised Heegner cycles modulo $p$, I: Modular curves ⋮ \(p^{\infty}\)-Selmer groups and rational points on CM elliptic curves ⋮ The universal \(p\)-adic Gross-Zagier formula
Cites Work
- Explicit Gross-Zagier and Waldspurger formulae
- \(p\)-adic \(L\)-functions for CM fields
- Serre's modularity conjecture. I
- Torsion points on curves and p-adic abelian integrals
- Heegner points and derivatives of \(L\)-series
- \(p\)-adic \(L\)-functions and rational points on elliptic curves with complex multiplication
- Higher congruences between modular forms
- Non-optimal levels of \(\text{mod }l\) modular representations
- Generalized Heegner cycles and \(p\)-adic Rankin \(L\)-series. With an appendix by Brian Conrad
- Fourier expansion of Arakawa lifting II: Relation with central L-values
- Local ε-Factors and Characters of GL(2)
- $\mathcal P$-adic modular forms over Shimura curves over totally real fields
- The Gross-Zagier Formula on Shimura Curves
- Locally analytic vectors in representations of locally 𝑝-adic analytic groups
- \(p\)-adic Fourier theory
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: A \(p\)-adic Waldspurger formula
