scholarly journals Arithmetic theory of $E$-operators

2016 ◽  
Vol 3 ◽  
pp. 31-65 ◽  
Author(s):  
Stéphane Fischler ◽  
Tanguy Rivoal
Keyword(s):  
Arithmetic Theory

scholarly journals Finding large Selmer rank via an arithmetic theory of local constants

2007 ◽  
Vol 166 (2) ◽  
pp. 579-612 ◽  
Author(s):  
Barry Mazur ◽  
Karl Rubin
Keyword(s):  
Arithmetic Theory

RÉPARTITION GALOISIENNE D'UNE CLASSE D'ISOGÉNIE DE COURBES ELLIPTIQUES

2012 ◽  
Vol 09 (02) ◽  
pp. 517-543
Author(s):  
RODOLPHE RICHARD
Keyword(s):  
New York ◽  
Elliptic Curves ◽  
Ergodic Theory ◽  
Mathematical Society ◽  
Princeton University ◽  
Galois Orbits ◽  
Theoretic Proof ◽  
Arithmetic Theory ◽  
Invent Math ◽  
Automorphic Functions

Dans cet article, on montre que les orbites sous Galois des invariants modulaires associés à des courbes elliptiques complexes sans multiplication complexe variant dans une même classe d'isogénie s'équidistribuent dans la courbe modulaire vers la probabilité hyperbolique. La démonstration repose sur des arguments de théorie ergodique, notamment le théorème de Ratner (cf. [A. Eskin et H. Oh, Ergodic theoretic proof of equidistribution of Hecke points, Ergodic Theory Dynam. Systems26(1) (2006) 163–167]), ainsi que sur le théorème de l'image ouverte de Serre [J.-P. Serre, Abelian l-Adic Representations and Elliptic Curves (W. A. Benjamin, New York, 1968); Propriétés Galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math.15(4) (1972) 259–331] dans le cas où les invariants modulaires considérés sont algébriques sur Q, et des résultats de G. Shimura dans le cas transcendant [Introduction to the Arithmetic Theory of Automorphic Functions, Publications of the Mathematical Society of Japan (Princeton University Press, Princeton, NJ, 1994)]. In this article, it is shown that Galois orbits of invariants associated with non-CM and pairwise isogeneous complex elliptic curves equidistribute in the classical modular curve towards the hyperbolic probability measure. The proof is based on arguments from ergodic theory, especially Ratner's theorem on unipotent flows (cf. [A. Eskin and H. Oh, Ergodic theoretic proof of equidistribution of Hecke points, Ergodic Theory Dynam. Systems26(1) (2006) 163–167]), as well as on Serre's open image theorem [J.-P. Serre, Abelian l-Adic Representations and Elliptic Curves (W. A. Benjamin, New York, 1968); Propriétés Galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math.15(4) (1972) 259–331] in case of algebraic invariants, and on G. Shimura's work in the transcendant case [Introduction to the Arithmetic Theory of Automorphic Functions, Publications of the Mathematical Society of Japan (Princeton University Press, Princeton, NJ, 1994)].

scholarly journals Game Edukasi Pengenalan dan Pembelajaran Berhitung untuk Siswa Kelas 1 Sekolah Dasar

2021 ◽  
Vol 11 (1) ◽  
pp. 47-59
Author(s):  
Muhammad Fikri Rivaldi ◽  
Yogiek Indra Kurniawan
Keyword(s):  
User Acceptance ◽  
Black Box ◽  
Educational Game ◽  
Acceptance Test ◽  
School Students ◽  
User Perceptions ◽  
Arithmetic Theory ◽  
Black Box Testing ◽  
Difficult Subject ◽  
Testing And Evaluation

Mathematics, especially arithmetic theory, is a difficult subject for most students. Apart from the theory that is difficult to understand, students also have shortcomings in the interest in learning materials and limitations in learning media to teach arithmetic theory in mathematics. The purpose of this research is to produce an educational game as an alternative to studying arithmetic material in mathematics. The target users of this educational game are grade 1 elementary school students. This game has several features, such as displaying material in the form of images and videos in the form of learning to count from numbers 1 to 10, and counting games with drag and drop. The method used to develop this application starts from design and planning, then continues with the material collection, implementation, testing and evaluation, and application maintenance. Based on black box testing, the results show that the educational game has been made as expected, while based on the User Acceptance Test, the results of user perceptions of the game are 94.25% with an indicator of the "Very Good" category which indicates that this educational game can be used as alternative in learning arithmetic theory in mathematics.

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