A new development of irrational number theory

Research Project

Project/Area Number	21540006
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	Algebra
Research Institution	Gunma University
Principal Investigator	AMOU Masaaki 群馬大学, 大学院・工学研究科, 教授 (60201901)
Project Period (FY)	2009 – 2011
Project Status	Completed (Fiscal Year 2011)
Budget Amount *help	¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000) Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000) Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000) Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords	無理数 / 超越数 / 代数的独立性 / 正規性 / パデ近似 / 消去法 / 超越測度
Research Abstract	For infinite product functions satisfying a chain of linear Mahler functional equations we established a useful sufficient condition for finiteness of the irrationality measure of the infinite product functions. We applied the condition to show a new criterion for algebraic independence of the values of the infinite product functions at the reciprocal of an integer. We also proved algebraic independence of the values of two infinite product functions at a general algebraic number by using elimination theory. Moreover, we investigate an axiomatic way of our method, which would have certain applications besides the infinite product functions.