Algebraic independence of the generating functions of the Stern polynomials and their twisted analogues

作者：Bundschuh Peter^*; Vaananen Keijo

来源：ARCHIV DER MATHEMATIK, 2015, 105(2): 139-148.

DOI：10.1007/s00013-015-0789-7

• Stern sequence and twisted version
• Polynomial analogues
• Generating functions
• Transcendence and algebraic independence
• Mahler's method

Dilcher and Stolarsky introduced and studied a polynomial analogue of Stern's diatomic sequence. Similarly, we define here a polynomial analogue of Bacher's twisted version of the Stern sequence. Our main aim is to consider the two-dimensional generating functions of both these polynomial sequences. More precisely, since they satisfy certain Mahler-type functional equations, we succeed in characterizing the algebraic independence over of the values of these two functions at algebraic points with 0 broken vertical bar xi broken vertical bar, broken vertical bar alpha broken vertical bar < 1

• 出版日期2015-8