Zeta elements for elliptic curves and applications
A Burungale, C Skinner, Y Tian, X Wan - arXiv preprint arXiv:2409.01350, 2024 - arxiv.org
Let $ E $ be an elliptic curve defined over $\mathbb {Q} $ with conductor $ N $ and $ p\nmid
2N $ a prime. Let $ L $ be an imaginary quadratic field with $ p $ split. We prove the …
2N $ a prime. Let $ L $ be an imaginary quadratic field with $ p $ split. We prove the …
p-adic L-functions and rational points on CM elliptic curves at inert primes
AA Burungale, S Kobayashi, K Ota - … of the Institute of Mathematics of …, 2024 - cambridge.org
Let K be an imaginary quadratic field and $ p\geq 5$ a rational prime inert in K. For a
$\mathbb {Q} $-curve E with complex multiplication by $\mathcal {O} _K $ and good …
$\mathbb {Q} $-curve E with complex multiplication by $\mathcal {O} _K $ and good …
Heegner points and Beilinson–Kato elements: a conjecture of Perrin-Riou
Heegner points and Beilinson–Kato elements: A conjecture of Perrin-Riou - ScienceDirect
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The universal p-adic Gross–Zagier formula
D Disegni - Inventiones mathematicae, 2022 - Springer
Let G be the group (GL 2× GU (1))/GL 1 over a totally real field F, and let X be a Hida family
for G. Revisiting a construction of Howard and Fouquet, we construct an explicit section P of …
for G. Revisiting a construction of Howard and Fouquet, we construct an explicit section P of …
On derivatives of Kato's Euler system for elliptic curves
D Burns, M Kurihara, T Sano - arXiv preprint arXiv:1910.07404, 2019 - arxiv.org
In this paper we study a new conjecture concerning Kato's Euler system of zeta elements for
elliptic curves $ E $ over $\mathbb {Q} $. This conjecture, which we refer to as …
elliptic curves $ E $ over $\mathbb {Q} $. This conjecture, which we refer to as …
On the theory of higher rank Euler, Kolyvagin and Stark systems, III: applications
D Burns, R Sakamoto, T Sano - arXiv preprint arXiv:1902.07002, 2019 - arxiv.org
In an earlier article we proved the existence of a canonical Kolyvagin derivative
homomorphism between the modules of Euler and Kolyvagin systems (in any given rank) …
homomorphism between the modules of Euler and Kolyvagin systems (in any given rank) …
Arithmetic of critical -adic -functions
D Benois, K Büyükboduk - arXiv preprint arXiv:2403.16076, 2024 - arxiv.org
Our objective in the present work is to develop a fairly complete arithmetic theory of critical $
p $-adic $ L $-functions on the eigencurve. To this end, we carry out the following tasks: a) …
p $-adic $ L $-functions on the eigencurve. To this end, we carry out the following tasks: a) …
Interpolation of Beilinson–Kato elements and p-adic L-functions
D Benois, K Büyükboduk - Annales mathématiques du Québec, 2022 - Springer
Our objective in this series of two articles, of which the present article is the first, is to give a
Perrin-Riou-style construction of p-adic L-functions (of Bellaïche and Stevens) over the …
Perrin-Riou-style construction of p-adic L-functions (of Bellaïche and Stevens) over the …
A higher Gross–Zagier formula and the structure of Selmer groups
CH Kim - Transactions of the American Mathematical Society, 2024 - ams.org
We describe a Kolyvagin system-theoretic refinement of Gross–Zagier formula by comparing
Heegner point Kolyvagin systems with Kurihara numbers when the root number of a rational …
Heegner point Kolyvagin systems with Kurihara numbers when the root number of a rational …
Refined applications of Kato's Euler systems for modular forms
CH Kim - arXiv preprint arXiv:2203.12157, 2022 - arxiv.org
We discuss refined applications of Kato's Euler systems for modular forms of higher weight
at good primes (with more emphasis on the non-ordinary ones) beyond the one-sided …
at good primes (with more emphasis on the non-ordinary ones) beyond the one-sided …