| Title | Q-linear dependence of certain Bessel moments |
| Authors | Zhou, Yajun |
| Affiliation | Princeton Univ, Program Appl & Computat Math PACM, Princeton, NJ 08544 USA Peking Univ, Acad Adv Interdisciplinary Studies AAIS, Beijing 100871, Peoples R China |
| Keywords | FEYNMAN-INTEGRALS REPRESENTATIONS CONJECTURES ROTATIONS |
| Issue Date | Apr-2021 |
| Publisher | RAMANUJAN JOURNAL |
| Abstract | Let I-0 and K-0 be modified Bessel functions of the zeroth order. We use Vanhove's differential operators for Feynman integrals to derive upper bounds for dimensions of the Q-vector space spanned by certain sequences of Bessel moments {integral(infinity)(0)[I-0(t)](a)[K-0(t)](b)t(2k+1)dt vertical bar k is an element of Z(>= 0)}, where a and b are fixed non-negative integers. For a is an element of Z boolean AND [1, b), our upper bound for the Q-linear dimension is [(a + b - 1)/2], which improves the Borwein-Salvy bound [(a + b + 1)/2]. Our new upper bound [(a + b - 1)/2] is not sharp for a = 2, b = 6, due to an exceptional Q-linear relation integral(infinity)(0)[I-0(t)](2)[K-0(t)](6)tdt = 72 integral(infinity)(0)[I-0(t)](2)[K-0(t)](6)t(3)dt, which is provable by integrating modular forms. |
| URI | http://hdl.handle.net/20.500.11897/612930 |
| ISSN | 1382-4090 |
| DOI | 10.1007/s11139-021-00416-9 |
| Indexed | SCI(E) |
| Appears in Collections: | 前沿交叉学科研究院 |
