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Galois theory on decompositions of spherical sets into spherical designs, and its analogy of number-theoretic theorems

Research Project

Project/Area Number 24K06688
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 11010:Algebra-related
Research InstitutionAichi University of Education

Principal Investigator

野崎 寛  愛知教育大学, 教育学部, 准教授 (80632778)

Project Period (FY) 2024-04-01 – 2029-03-31
Project Status Granted (Fiscal Year 2024)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2028: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2027: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2026: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2025: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2024: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords球面デザイン / 正則グラフ / ガロア理論 / ゼータ関数
Outline of Research at the Start

Stark-Terras(1996, 2000, 2007)は有限グラフのcovering と閉路に「素数」の概念を導入し,数論におけるガロア理論と,ゼータ関数,素数定理を含む周辺の定理の類似を得た.一方,有限正則グラフと球面有限集合にはある種の「双対」な関係があり,隣接行列とグラム行列,内周とデザインの強さなどを対応させ,双方において同様の定理を得られることがある.本研究の目的は,球面有限集合のある種の良い分割をcovering の双対と見て,Stark-Terras が与えた有限正則グラフにおける各数論定理類似の双対版を与えることである.

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Published: 2024-04-05   Modified: 2024-06-24  

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