Comptes Rendus
no. 2
Number theory
Growth of class numbers of positive definite ternary unimodular Hermitian lattices over imaginary number fields
[Croissance du nombre de classes de réseaux hermitiens unimodulaires sur un corps quadratique imaginaire]

Présenté par : the Editorial Board

Byeong Moon Kim1 ; Poo-Sung Park2
1 Department of Mathematics, Gangnung-Wonju National University, Gangneung Daehangno 120, Gangneung City, Gangwon Province, 210-702, Republic of Korea
2 Department of Mathematics Education, Kyungnam University, Changwon, 631-701, Republic of Korea
Comptes Rendus. Mathématique, Volume 355 (2017) no. 2, pp. 119-122.

Nous donnons une borne inférieure pour le nombre de classes de réseaux ternaires hermitiens unimodulaires sur corps quadratique imaginaire. Cela montre que le nombre de classes de réseaux unimodulaires hermitienne tend vers l'infini avec le discriminant du corps.

We give a lower bound for class numbers of unimodular ternary Hermitian lattices over imaginary quadratic fields. This shows that class numbers of unimodular Hermitian lattices grow infinitely as the field discriminants grow.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.12.008
Byeong Moon Kim 1 ; Poo-Sung Park 2

1 Department of Mathematics, Gangnung-Wonju National University, Gangneung Daehangno 120, Gangneung City, Gangwon Province, 210-702, Republic of Korea
2 Department of Mathematics Education, Kyungnam University, Changwon, 631-701, Republic of Korea 
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Byeong Moon Kim; Poo-Sung Park. Growth of class numbers of positive definite ternary unimodular Hermitian lattices over imaginary number fields. Comptes Rendus. Mathématique, Volume 355 (2017) no. 2, pp. 119-122. doi : 10.1016/j.crma.2016.12.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.12.008/

[1] L.J. Gerstein Integral decomposition of Hermitian forms, Amer. J. Math., Volume 92 (1970), pp. 398-418

[2] K. Hashimoto; H. Koseki Class numbers of positive definite binary and ternary unimodular Hermitian forms, Tohoku Math. J. (2), Volume 41 (1989) no. 2, pp. 171-216

[3] J.S. Hsia; J.P. Prieto-Cox Representations of positive definite Hermitian forms with approximation and primitive properties, J. Number Theory, Volume 47 (1994) no. 2, pp. 175-189

[4] N. Jacobson A note on Hermitian forms, Bull. Amer. Math. Soc., Volume 46 (1940), pp. 264-268

[5] A.A. Johnson Integral representation of Hermitian forms over local fields, J. Reine Angew. Math., Volume 229 (1968), pp. 57-80

[6] M.-H. Kim; P.-S. Park 2-Universal Hermitian lattices over imaginary quadratic fields, Ramanujan J., Volume 22 (2010) no. 2, pp. 139-151

[7] B.M. Kim; M.-H. Kim; B.-K. Oh A finiteness theorem for representability of quadratic forms by forms, J. Reine Angew. Math., Volume 581 (2005), pp. 23-30

[8] W. Landherr Äquivalenz Hermitscher Formen über einen beliebigen algebraischen Zahlkörper, Abh. Math. Semin. Univ. Hamb., Volume 11 (1935), pp. 245-248

[9] O.T. O'Meara Introduction to Quadratic Forms, Springer-Verlag, New York, 1973

[10] G. Robin Estimation de la fonction de Tchebychef θ sur le k-ième nombre premier et grandes valeurs de la fonction ω(n) nombre de diviseurs premiers de n, Acta Arith., Volume 42 (1983) no. 4, pp. 367-389

[11] A. Schiemann Classification of Hermitian forms with the neighbour method, J. Symb. Comput., Volume 26 (1998) no. 4, pp. 487-508

[12] G. Shimura Arithmetic of unitary groups, Ann. Math. (2), Volume 79 (1964), pp. 369-409

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