An asymptotic behavior of solutions of p-adic differential equations

Research Project

Project/Area Number	15H06261
Research Category	Grant-in-Aid for Research Activity Start-up
Allocation Type	Single-year Grants
Research Field	Algebra
Research Institution	Nagoya University
Principal Investigator	Ohkubo Shun 名古屋大学, 多元数理科学研究科, 助教 (20755160)
Project Period (FY)	2015-08-28 – 2017-03-31
Project Status	Completed (Fiscal Year 2016)
Budget Amount *help	¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000) Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000) Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords	p進微分方程式 / Gauss-Manin接続
Outline of Final Research Achievements	We studied Chiarellotto-Tsuzuki's conjecture on the growth of solutions of p-adic differential equations with Frobenius structures over open unit ball. Our basic approach is based on the author's previous work (2017, Adv. Math.) using certain cyclic vectors with respect to Frobenius structures. In the article written by T. Nakagawa（2013、Tohoku), we found a certain condition on the determination of the growth. We considered a related condition to Nakagawa's condition, and for rank~3 differential equation satisfies this condition, we could verify Chiarellotto-Tsuzuki's conjecture.

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