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http://dx.doi.org/10.4134/BKMS.2005.42.3.639

THE CLASS NUMBER OF ORDERS IN A QUATERNION ALGEBRA OVER A DYADIC LOCAL FIELD  

Jun, Sung-Tae (DIVISION OF MATHEMATICS AND COMPUTER SCIENCE, KONKUK UNIVERSITY)
Kim, In-Suk (DEPARTMENT OF MATHEMATICS EDUCATION, WONKWANG UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.42, no.3, 2005 , pp. 639-652 More about this Journal
Abstract
We find the class number of orders in a quaternion algebra over a dyadic local field.
Keywords
quaternion algebra; order; class number; normalizer;
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  • Reference
1 M. Deuring, Die An zahl der Typen von Maximalordnungen einer definitn Quaternionalgebra mit primer Grundzahl, Jber. Deutsch. Math. Verein. 54 (1950), 24-41
2 M. Eichler, The basis problem for modular forms and the traces of Hecke operators, Springer-Verlag, Lecture Notes in Math. 320 (1972), 75-151
3 H. Hijikata, Explicit formula of the traces of the Hecke operators for ${\Gamma}_0$(N), J. Math. Soc. Japan 26 (1974), 56-82   DOI
4 H. Hijikata, A. Pizer, and T. Shemanske, Orders in Quaternion Algebras, J. Reine Angew Math. 394 (1989), 59-106
5 A. Atkin and J. Lehner, Hecke operators on ${\Gamma}_0$(N), Math. Ann. 185 (1970), 134-160   DOI
6 A. Pizer, An Algorithm for computing modular forms on ${\Gamma}_0$(N), J. Algebra 64 (1980), 340-390   DOI
7 S. Jun, Mass formula of an order over a dyadic local field, preprint
8 A. Pizer, On the arithmetic of Quaternion algebras II , J. Math. Soc. Japan 28 (1976), 676-698   DOI
9 A. Pizer, The action of the Canonical involution on Modular forms of weigh 2 on ${\Gamma}_0$(N), Math. Ann. 226 (1977), 99-116   DOI
10 I. Reiner, Maximal orders, Academic Press, 1975
11 S. Jun, On the certain primitive orders J. Korean Math. Soc. 4 (1995), 473-481
12 T. tamagawa, On the trace formula, J. Fac. Sci. Univ. Tokyo Sec. I (1960), 363- 380
13 A. Weil, Basic number theory, Berlin, Hedelberg, New York, Springer, 1967