| Project/Area Number |
15K17504
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Hirosaki University |
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Principal Investigator |
Tachiya Yohei 弘前大学, 理工学研究科, 准教授 (90439539)
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| Research Collaborator |
Luca Florian University of the Witwatersrand, Professor
Coons Michael University of Newcastle, Senior Lecturer
Elsner Carsten University of Applied Science FHDW, Professor
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 整数論 / 無理数 / 超越数 / ランベルト級数 / テータ関数 / 保型形式 / テータ零値 / 従属関係式 / 代数的独立性 / 超越性 / 無理性 / フィボナッチ数 / 線形独立性 / ベキ級数 / ディオファンタス近似 / β展開 / ヤコビテータ関数 / ディリクレ指標 / フィボナッチ・ゼータ関数 |
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| Outline of Final Research Achievements |
We studied and obtained a refinement of Erdos's theorem(1948), which gives some structural properties for the q-ary expansion of Lambert series. In particular, we obtained linear independence results for the reciprocal sums of binary recurrences associated with Dirichlet characters. Furthermore we investigated arithmetical properties for some analytic functions and showed that taking an asymptotic viewpoint allows one to prove much stronger transcendence statements in many general situations.
We also studied algebraic properties of the classical theta-constants and gave explicit algebraic dependence relations in some particular cases. This yields algebraic independence results for certain values of the theta-constants and the transcendence results for certain Lambert series.
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