Algebraic independence of the values of the Hecke–Mahler series and its derivatives at algebraic numbers
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- Taka-aki Tanaka
- Department of Mathematics, Keio University, Hiyoshi 3-14-1, Kohoku-ku, Yokohama 223-8522, Japan
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- Yusuke Tanuma
- Department of Mathematics, Keio University, Hiyoshi 3-14-1, Kohoku-ku, Yokohama 223-8522, Japan
抄録
<jats:p> We show that the Hecke–Mahler series, the generating function of the sequence [Formula: see text] for [Formula: see text] real, has the following property: Its values and its derivatives of any order, at any nonzero distinct algebraic numbers inside the unit circle, are algebraically independent if [Formula: see text] is a quadratic irrational number satisfying a suitable condition. </jats:p>
収録刊行物
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- International Journal of Number Theory
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International Journal of Number Theory 14 (09), 2369-2384, 2018-09-18
World Scientific Pub Co Pte Lt
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詳細情報 詳細情報について
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- CRID
- 1360004236173865344
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- ISSN
- 17937310
- 17930421
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- データソース種別
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- Crossref
- KAKEN