| Project/Area Number |
09640036
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tottori University |
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Principal Investigator |
HARASE Takashi Tottori Univ., Dept. of Education, Professor, 教育地域科学部, 教授 (90016056)
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| Co-Investigator(Kenkyū-buntansha) |
GOTO Kazuo Tottori Univ., Dept. of Education, Assistant Professor, 教育地域科学部, 助教授 (00140533)
KOJIMA Masatoshi Tottori Univ., Dept. of Education, Professor, 教育地域科学部, 教授 (90032317)
KURIBAYASHI Yukio Tottori Univ., Dept. of Education, Professor, 教育学部, 教授 (30031909)
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| Project Period (FY) |
1997 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1999: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1998: ¥500,000 (Direct Cost: ¥500,000)
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| Keywords | finite field / positive characteristic / algebraic / rational series / recognizable / discrepancy / language / uniform distribution / recognizable / continued fraction / code theory / random number / positivl charateristic / algebiaic / rationcl series / rewgnizable / cude theory / rational series / continned fraction / F_p |
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| Research Abstract |
We define a mapping Φ from the monomials in κ[[z]] to XィイD3*(/)qィエD3ィイD2mィエD2 by the following : if l ≠ 0 then
Φ(zィイD3i1(/)1ィエD3zィイD3i2(/)2ィエD3...zィイD3im(/)mィエD3) = xィイD2rィエD2ィイD21lィエD2ィイD1rィエD1ィイD22l...ィエD2ィイD1rィエD1ィイD2mlィエD2xィイD2rィエD2ィイD21,l-1ィエD2ィイD1rィエD1ィイD22,l-1...ィエD2ィイD1rィエD1ィイD2m,l-1ィエD2...xィイD2rィエD2ィイD211ィエD2ィイD1rィエD1ィイD221...ィエD2ィイD1rィエD1ィイD2m1ィエD2,
and Φ(1) = 1, where XィイD2qィエD2ィイD1mィエD1 = {xィイD2rィエD2ィイD21ィエD2ィイD1rィエD1ィイD22....ィエD2ィイD1rィエD1ィイD2mィエD2|0≦rィイD21ィエD2,rィイD22ィエD2,...,rィイD2mィエD2≦q-1} with indeterminates xィイD2rィエD2ィイD21ィエD2ィイD1rィエD1ィイD22...ィエD2ィイD1rィエD1ィイD2mィエD2.
Extending Phi-linearly, our main results are the followings
Theorem. If f ∈ FィイD2qィエD2[[z]] is algebraic, then Φ(f) is rational in FィイD2qィエD2≪XィイD2qィエD2ィイD1mィエD1≫.
Corollary 1. If f = ΣィイD2nィエD2aィイD2nィエD2zィイD1nィエD1 ∈ FィイD2qィエD2[[zィイD21ィエD2,aィイD22ィエD2,...,zィイD2mィエD2]] is algebraic, then it follows that ΣィイD5nィエD5aィイD2nィエD2zィイD1|n|ィエD1 ∈ FィイD2qィエD2(z).
Here |n| denotes the length of digits in base q expression of n.
Investigator K.Goto obtained several new results on uniform distribution theory.
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