Horizontal non-vanishing of Heegner points and toric periods

DOI10.1016/j.aim.2019.106938zbMath1452.11075arXiv1712.01465OpenAlexW2998627664WikidataQ126461565 ScholiaQ126461565MaRDI QIDQ2287940

Ye Tian, Ashay A. Burungale

Publication date: 22 January 2020

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.01465

zbMATH Keywords

Heegner pointsGross-Zagier formulaWaldspurger formulatoric periods

Mathematics Subject Classification ID

Arithmetic aspects of modular and Shimura varieties (11G18) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Related Items (5)

The congruent number problem and elliptic curves ⋮ Quantitative non-vanishing of Dirichlet \(L\)-values modulo \(p\) ⋮ On the non-vanishing of \(p\)-adic heights on CM abelian varieties, and the arithmetic of Katz \(p\)-adic \(L\)-functions ⋮ On the non-triviality of the $p$-adic Abel–Jacobi image of generalised Heegner cycles modulo $p$, I: Modular curves ⋮ Intersection of class fields

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Explicit Gross-Zagier and Waldspurger formulae
• A nonsplit sum of coefficients of modular forms
• Sparse equidistribution problems, period bounds and subconvexity
• Heegner points and derivatives of \(L\)-series
• Twists of modular forms and endomorphisms of abelian varieties
• On some arithmetic properties of modular forms of one and several variables
• On the local Langlands conjecture for GL(2)
• The subconvexity problem for \(\mathrm{GL}_2\)
• The André-Oort conjecture for \(\mathcal A_g\)
• Faltings heights of abelian varieties with complex multiplication
• On the averaged Colmez conjecture
• The subconvexity problem for Rankin-Selberg \(L\)-functions and equidistribution of Heegner points
• Mod \(pq\) Galois representations and Serre's conjecture
• A \(p\)-adic Waldspurger formula
• Non-triviality of generalised Heegner cycles over anticyclotomic towers: a survey
• Level Raising and Anticyclotomic Selmer Groups for Hilbert Modular Forms of Weight Two
• ANDRÉ–OORT CONJECTURE AND NONVANISHING OF CENTRAL -VALUES OVER HILBERT CLASS FIELDS
• ON THE NON-TRIVIALITY OF THE -ADIC ABEL–JACOBI IMAGE OF GENERALISED HEEGNER CYCLES MODULO , II: SHIMURA CURVES
• Local ε-Factors and Characters of GL(2)
• Sur le rang des courbes elliptiques sur les corps de classes de Hilbert
• On the non-triviality of the $p$-adic Abel–Jacobi image of generalised Heegner cycles modulo $p$, I: Modular curves

This page was built for publication: Horizontal non-vanishing of Heegner points and toric periods