Uniform distribution of Heegner points

By V. Vatsal. 2002

146 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8ba7fab96a0ceb1b09bd2aa1469ae460c9ea69a8

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In Algebra and Number Theory

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Citations in the corpus

Distribution of lattice orbits on homogeneous varieties (2004, background): “The distribution of SL(2, Z)-orbits in V was considered by Nogueira [N], and the case of a general lattice by Ledrappier [L].”
Equidistribution, L-functions and ergodic theory: on some problems of Yu. Linnik (2006, result): “A few years ago, Vatsal and Cornut [16], [73], [74] used period relations and equidistribution in a similar way to obtain somewhat stronger non-vanishing results for Rankin–Selberg L-functions but associated to anti-cyclotomic2 characters of a fixed imaginary quadratic field.”
Gross-Zagier Formula for GL(2), II (2004, background): “See the papers [1; 11] of Bertolini–Darmon and Vatsal for details.”
Mazur’s conjecture on higher Heegner points (2002, methodology): “This very same map also arises in the context of Gross points on definite Shimura curves [19], and we then follow Vatsal’s proof with only minor improvements: put G = PSL2(Qp), Γ1 = ∏σ∈R Γ(1)σ , and let ∆ be the diagonal in G.”
L -functions and Galois Representations: Nontriviality of Rankin-Selberg L -functions and CM points (2007, background): “The basic ideas are drawn from our previous papers [4, 26, 27] with a few simplifications and generalizations.”
Central L-Values and Toric Periods for GL(2) (2009, background): “For more arithmetic applications of such formulas, see for example, [2], [21], and [19].”
On anticyclotomic μ-invariants of modular forms (2006, methodology): “Using results of Ribet–Takahashi [28, 29] on degrees of modular parameterizations arising from Shimura curves, we establish that (1) ordp ( ηf (N) ξf (N+, N−) ) = ∑ q|N− tf (q) and thus deduce the µ-part of the main conjecture in both the ordinary and supersingular case.”
Sparse equidistribution problems, period bounds and subconvexity (2005, background): “A more striking example is Vatsal’s use of equidistribution to prove nonvanishing results [45].”
Iwasawa's Main Conjecture for elliptic curves over anticyclotomic Zp-extensions (2005, methodology): “For example, Vatsal has shown ([ Va1 , Th. 1.4]) that L(E/K, χ,1) is nonzero for almost all χ when χ varies over the anticyclotomic characters of p-power conductor for a fixed p.”
Distribution of periodic torus orbits and Duke's theorem for cubic fields (2007, background): “[44] V. Vatsal, Uniform distribution of Heegner points, Invent.”
Variation of Heegner points in Hida families (2006, methodology): “The precise result, Corollary 3.1.2, is actually somewhat stronger and extends Cornut and Vatsal’s proof of Mazur’s conjecture on the nonvanishing of Heegner points from the case of modular forms of weight two and trivial character to all ordinary modular forms.”
CM points and quaternion algebras (2005, background): “In fact, the irrationality arguments given by Ferrero and Washington were the original motivation for the introduction in [18] of rational and irrational elements to the study of CM points.”
Finding Large Selmer Rank via an Arithmetic Theory of Local Constants (2005, background): “anticyclotomic Zp-extension of K, and thanks to [Co] and [ V ] we know that the bulk of the contribution to the Selmer groups in Theorem 8.3 comes from Heegner points.”
Special values of anticyclotomic $L$-functions (2003, methodology): “For a discussion of the analogies, we refer the reader to the introduction of [Vat01].”