Construction and Approximation of the Polyatomic Bitemperature Euler System

2018 ◽  
pp. 85-96
Author(s):  
Denise Aregba-Driollet ◽  
Stéphane Brull
Keyword(s):  
Euler System

scholarly journals Iwasawa Theory of Elliptic Modular Forms Over Imaginary Quadratic Fields at Non-ordinary Primes

2019 ◽  
Author(s):  
Kâzım Büyükboduk ◽  
Antonio Lei
Keyword(s):  
Modular Form ◽  
Modular Forms ◽  
Quadratic Field ◽  
Euler System ◽  
Base Change ◽  
Iwasawa Theory ◽  
Imaginary Quadratic Field ◽  
Selmer Groups ◽  
Imaginary Quadratic Fields ◽  
Elliptic Modular Form

AbstractThis article is a continuation of our previous work [7] on the Iwasawa theory of an elliptic modular form over an imaginary quadratic field $K$, where the modular form in question was assumed to be ordinary at a fixed odd prime $p$. We formulate integral Iwasawa main conjectures at non-ordinary primes $p$ for suitable twists of the base change of a newform $f$ to an imaginary quadratic field $K$ where $p$ splits, over the cyclotomic ${\mathbb{Z}}_p$-extension, the anticyclotomic ${\mathbb{Z}}_p$-extensions (in both the definite and the indefinite cases) as well as the ${\mathbb{Z}}_p^2$-extension of $K$. In order to do so, we define Kobayashi–Sprung-style signed Coleman maps, which we use to introduce doubly signed Selmer groups. In the same spirit, we construct signed (integral) Beilinson–Flach elements (out of the collection of unbounded Beilinson–Flach elements of Loeffler–Zerbes), which we use to define doubly signed $p$-adic $L$-functions. The main conjecture then relates these two sets of objects. Furthermore, we show that the integral Beilinson–Flach elements form a locally restricted Euler system, which in turn allow us to deduce (under certain technical assumptions) one inclusion in each one of the four main conjectures we formulate here (which may be turned into equalities in favorable circumstances).

scholarly journals On the Bloch–Kato conjecture for Hilbert modular forms

2021 ◽  
Author(s):  
Matteo Tamiozzo
Keyword(s):  
Modular Forms ◽  
Automorphic Forms ◽  
Euler System ◽  
Central Point ◽  
Shimura Curves ◽  
Hilbert Modular Forms ◽  
Reciprocity Laws ◽  
Hilbert Modular ◽  
Special Points

AbstractThe aim of this paper is to prove inequalities towards instances of the Bloch–Kato conjecture for Hilbert modular forms of parallel weight two, when the order of vanishing of the L-function at the central point is zero or one. We achieve this implementing an inductive Euler system argument which relies on explicit reciprocity laws for cohomology classes constructed using congruences of automorphic forms and special points on several Shimura curves.

Sharp Dimension Estimates for the Attractors of the Regularized Damped Euler System

2021 ◽  
Vol 104 (1) ◽  
pp. 169-172
Author(s):  
S. V. Zelik ◽  
A. A. Ilyin ◽  
A. G. Kostianko
Keyword(s):  
Euler System

scholarly journals Relaxation schemes for the multicomponent Euler system

2003 ◽  
Vol 37 (6) ◽  
pp. 909-936 ◽  
Author(s):  
Stéphane Dellacherie
Keyword(s):  
Euler System ◽  
Relaxation Schemes

scholarly journals The Finite Volume WENO with Lax–Wendroff Scheme for Nonlinear System of Euler Equations

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 211 ◽  
Author(s):  
Haoyu Dong ◽  
Changna Lu ◽  
Hongwei Yang
Keyword(s):  
Finite Volume ◽  
Time Discretization ◽  
Euler System ◽  
Weno Scheme ◽  
Local Characteristic ◽  
Finite Volume Scheme ◽  
Mesh Structure ◽  
Hyperbolic Conservation Law ◽  
Higher Derivative ◽  
Accuracy Order

We develop a Lax–Wendroff scheme on time discretization procedure for finite volume weighted essentially non-oscillatory schemes, which is used to simulate hyperbolic conservation law. We put more focus on the implementation of one-dimensional and two-dimensional nonlinear systems of Euler functions. The scheme can keep avoiding the local characteristic decompositions for higher derivative terms in Taylor expansion, even omit partly procedure of the nonlinear weights. Extensive simulations are performed, which show that the fifth order finite volume WENO (Weighted Essentially Non-oscillatory) schemes based on Lax–Wendroff-type time discretization provide a higher accuracy order, non-oscillatory properties and more cost efficiency than WENO scheme based on Runge–Kutta time discretization for certain problems. Those conclusions almost agree with that of finite difference WENO schemes based on Lax–Wendroff time discretization for Euler system, while finite volume scheme has more flexible mesh structure, especially for unstructured meshes.

scholarly journals Kato's Euler system and the Mazur-Tate refined conjecture of BSD type

2018 ◽  
Vol 140 (2) ◽  
pp. 495-542 ◽  
Author(s):  
Kazuto Ota
Keyword(s):  
Euler System

Kato’s Euler system and rational points on elliptic curves I: A p-adic Beilinson formula

2013 ◽  
Vol 199 (1) ◽  
pp. 163-188 ◽  
Author(s):  
Massimo Bertolini ◽  
Henri Darmon
Keyword(s):  
Elliptic Curves ◽  
Rational Points ◽  
Euler System
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