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ON THE ORDERS IN A QUATERNION ALGEBRA OVER A DYADIC LOCAL FIELD
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  • Journal title : Honam Mathematical Journal
  • Volume 31, Issue 4,  2009, pp.611-632
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2009.31.4.611
 Title & Authors
ON THE ORDERS IN A QUATERNION ALGEBRA OVER A DYADIC LOCAL FIELD
Jun, Sung-Tae; Kim, In-Suk;
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 Abstract
The orders in a quaternion algebra play a central role of the theory of Hecke operators. In this paper, we study the arithmetic properties of optimal embeddings of orders in a quaternion algebra over a dyadic local field.
 Keywords
order;quaternion algebra;normalizer;optimal embedding;
 Language
English
 Cited by
1.
ZETA FUNCTIONS ON A CETAIN ORDERS IN A QUATERNION ALGEBRA,;;

한국수학교육학회지시리즈B:순수및응용수학, 2012. vol.19. 3, pp.297-304 crossref(new window)
1.
ZETA FUNCTIONS ON A CETAIN ORDERS IN A QUATERNION ALGEBRA, The Pure and Applied Mathematics, 2012, 19, 3, 297  crossref(new windwow)
 References
1.
J. Brzezinski, On automorphisms of quatenlion orders J. reine angew. Math. 403(1990) 166-186 crossref(new window)

2.
J. Brzezinski, On embedding numbers into quaternion orders Comment. Math. Helvetici 66(1991) 302-318. crossref(new window)

3.
M. Deuring, Die An zahl der Typen von Marimalordnungen einer definitn Quaternionalgebra mit primer Gnmdzahl. Jber. Deutsch. Math. Verein. Vol.54, pp.24-41, 1950.

4.
M. Eichler, The basis problem f or modular forms and the traces of Hecke operators. Springer-Verlag, Lecture Notes in Math., Vol.320, pp.75-151, 1972. crossref(new window)

5.
H. Hijikata, Explicit formula of the traces of the Hecke operators for ${\Gamma}_{0}$(N), J. Math. Soc. Japan, Vol. 26, pp. 56-82, 1974. crossref(new window)

6.
H. Hijikara, A. Pizer and T. Shemanske, Orders in Quaternion Algebras, J. Reine angew Math., Volbf 394 1989, pp.59-106

7.
S. Jun. The class number of orders in a quaternion algebra over a dyadic local field Bull. KMS. Vol. 42, No.3 pp. 639-652, 2005. crossref(new window)

8.
S. Jun, The Maxx formula of orders over a dyadic local field Commun. KMS, Vol.20, No. 2 pp.231-238

9.
S. Jun, On the cert ain Primitive orders J. Korean Math. Soc. Vol. 34, No.4, pp.791-807, 1997.

10.
A. Pizer, On the arithmetic of Quaternion algebras II J. Math. Soc. Japan Vol.28, pp.676-698, 1976. crossref(new window)

11.
A. Pizer, The action of the Canonical involution on Modular forms of weigh 2 on ${\Gamma}_{0}$(N) Math. Ann. Vol. 226, pp.99-116, 1977. crossref(new window)

12.
A. Pizer, An Algorithm for computing modular forms on ${\gamma}_{0}$(N) J. Algebra Vol.64, pp. 340-390, 1980. crossref(new window)

13.
I. Reiner, Maximal orders Academic Press, 1975.

14.
A. Weil, Basic number theory Berlin, Hedelberg, New York: Springer 1957.