1997 Fiscal Year Final Research Report Summary
Experimental Method of Mathematics
| Project/Area Number |
08404008
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Osaka University |
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Principal Investigator |
YAMAMOTO Yoshihiko Grad.School of Sci., Osaka University, Prof., 大学院・理学研究科, 教授 (90028184)
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| Co-Investigator(Kenkyū-buntansha) |
OHYAMA Yohsuke Grad.School of Sci., Osaka University, Assist., 大学院・理学研究科, 助手 (10221839)
MURAKAMI Jun Grad.School of Sci., Osaka University, Assoc.Prof., 大学院・理学研究科, 助教授 (90157751)
KOMATSU Gen Grad.School of Sci., Osaka University, Assoc.Prof., 大学院・理学研究科, 助教授 (60108446)
MATSUMURA Akitaka Grad.School of Sci., Osaka University, Prof., 大学院・理学研究科, 教授 (60115938)
HIBI Takayuki Grad.School of Sci., Osaka University, Prof., 大学院・理学研究科, 教授 (80181113)
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| Project Period (FY) |
1996 – 1997
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| Keywords | Computer algbra / Limit-formula / Elliptic curve / Taniyama-Shumura conjecture / Automorphic function / Class fields / Riemann surface |
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| Research Abstract |
We worked, by usisng softwares for the computer algebra, manily in the fields of arithmetics, algebraic geometry, automorphic functions, Riemann surfaces and cryptosystems and gots many interesting results, some of them are as follows :
1. Algebraic Number Thoery : (1) Computation of classnumbers and fundamental units of number fields. (2) Relations between certain residule class groups of real quadratic fields and class groups of imaginary quadratic fields. (3) Numerical computations of Kronecker's limit-formula of real quadratic fields. (4) Group structures of the unit groups of Dihedral extensions over the rational number field.
2. Arithmetics in elliptic curves defined over the rational field : (1) Existence of the canonical parameters and canonical power series solutions, (2) Uniformizaton of elliptic curves by automorphic functions. (3) Algorithmic Computation of canonical power series and the global zeta-function over the ring of rational integers. (4) Existence of canonical arithmetic-structures in elliptic curves.
3. Application of 3D-graphical representation of complex functions : (1) Represatations of Riemann surfaces by Complex Plot commands. (2) Investigating periodical properties of complex functions given by power series. (3) Automorphic properties of canonical power seires of elliptic curves.
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