Special values of anticyclotomic $L$-functions

By V. Vatsal. 2003

141 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/24ccdaab318db2c2de9744958135f172faa47971

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. M. Bertolini
2. C. Cornut
3. Robert H. Pollack
4. T. Weston
5. Henri Darmon
6. V. Vatsal
7. Karl Rubin
8. C. Skinner

In Geometry and Topology

1. M. Bertolini
2. Henri Darmon
3. C. Skinner
4. C. Cornut
5. Robert H. Pollack
6. T. Weston
7. Karl Rubin
8. V. Vatsal

Citations in the corpus

• L -functions and Galois Representations: Nontriviality of Rankin-Selberg L -functions and CM points (2007, methodology): “This may be proved by induction, exactly as in Proposition 5.3 of [ 27 ], or Lemma 4.15 above in the indefinite case.”
• CM points and quaternion algebras (2005, result): “Although the statements are somewhat complicated, they are not hard to prove, in view of our earlier results [2], [18], [ 19 ], where all the main ideas are already present.”
• Ranks of elliptic curves (2002, result): “What Nekov a r proved (using recent results of Vatsal [ 74 ] and Cornut [10]) is that if p is a prime not dividing #E(Q)tors ,a nd ifE has good ordinary reduction at p (see Chapters V and VII of [68]), then dimFp Sp(E) and rankan(E )h ave the same parity.”
• Selmer groups and the indivisibility of Heegner points (2014, unknown): “which can be essentially deduced from the work of Vatsal [43] and Bertolini– Darmon [4].”
• Iwasawa's Main Conjecture for elliptic curves over anticyclotomic Zp-extensions (2005, methodology): “The proof given here follows closely the approach in [ Va2 ], avoiding the study of certain groups of connected components which was involved in the methods of [BD5].”
• Multiplicative reduction and the cyclotomic main conjecture for GL2 (2014, background): “We also explain that the reference to [20] in [18] should have been augmented with a reference to [4].”
• 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.”