G関数のHermite-Pade近似を用いた周期予想へのアプローチ

• Project/Area Number: 24K16905
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 11010:Algebra-related
• Research Institution: Meiji Gakuin University
• Principal Investigator: 川島 誠 明治学院大学, 情報数理学部, 講師 (70818129)
• Project Period (FY): 2024-04-01 – 2029-03-31
• Project Status: Granted (Fiscal Year 2024)
• Budget Amount: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000); Fiscal Year 2028: ¥130,000 (Direct Cost: ¥100,000、Indirect Cost: ¥30,000); Fiscal Year 2027: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2026: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2025: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2024: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 線形独立性 / 代数的独立性 / 周期予想 / 超越数論

Outline of Research at the Start

SiegelのG関数の近似の具体的構成に基づいて、一般超幾何関数をはじめとする様々なG関数の特殊値の間に線形独立性や代数的独立性が成り立つことを示す。