论文标题
对奇数多个谐波总和的完整性和一些评估
Integrality and some evaluations of odd multiple harmonic sums
论文作者
论文摘要
在2015年，S。Hong和C. Wang证明，当$ N \ GEQ 2 $时，没有任何基本对称功能，\ ldots，1/（2n-1）$。 2017年，KH。 Pilehrood，T。Pilehrood和R. Tauraso证明了多个谐波总和$ h_n（s_1，\ ldots，s_r）$绝不是整数，除了$ h_1（s_1）= 1 $和$ h_3（s_1）= 1 $和$ h_3（1,1）= 1 $。他们还证明，当$ n \ geq 2 $ $ n \ geq 2 $时，多个谐波恒星总和绝不是整数。在本文中，我们考虑了奇怪的多个谐波总和和奇怪的谐波星和奇数，并表明这些总和都不是一个整数，除了琐碎的情况外。此外，我们对具有深度的奇数（交替）多个谐波总和进行评估。
In 2015, S. Hong and C. Wang proved that none of the elementary symmetric functions of $1,1/3,\ldots,1/(2n-1)$ is an integer when $n\geq 2$. In 2017, Kh. Pilehrood, T. Pilehrood and R. Tauraso proved that the multiple harmonic sums $H_n(s_1,\ldots,s_r)$ are never integers with exceptions of $H_1(s_1)=1$ and $H_3(1,1)=1$. They also proved that the multiple harmonic star sums are never integers when $n\geq 2$. In this paper, we consider the odd multiple harmonic sums and the odd multiple harmonic star sums and show that none of these sums is an integer with exception of the trivial case. Besides, we give evaluations of the odd (alternating) multiple harmonic sums with depth one.
