南方科技大学知识苑(SUSTech KC): On sums of coefficients of polynomials related to the Borwein conjectures

题名	On sums of coefficients of polynomials related to the Borwein conjectures
作者	Goswami, Ankush 1; Pantangi, Venkata Raghu Tej2
通讯作者	Goswami, Ankush
发表日期	2021-02-01
DOI	10.1007/s11139-020-00352-0
发表期刊	RAMANUJAN JOURNAL 影响因子和分区
ISSN	1382-4090
EISSN	1572-9303
卷号	57 期号:1
摘要	Recently, Li (Int J Number Theory, 2020) obtained an asymptotic formula for a certain partial sum involving coefficients for the polynomial in the First Borwein conjecture. As a consequence, he showed the positivity of this sum. His result was based on a sieving principle discovered by himself and Wan (Sci China Math, 2010). In fact, Li points out in his paper that his method can be generalized to prove an asymptotic formula for a general partial sum involving coefficients for any prime p>3. In this work, we extend Li's method to obtain asymptotic formula for several partial sums of coefficients of a very general polynomial. We find that in the special cases p=3,5, the signs of these sums are onsistent with the three famous Borwein conjectures. Similar sums have been studied earlier by Zaharescu (Ramanujan J, 2006) using a completely different method. We also improve on the error terms in the asymptotic formula for Li and Zaharescu. Using a recent result of Borwein (JNT 1993), we also obtain an asymptotic estimate for the maximum of the absolute value of these coefficients for primes p=2,3,5,7,11,13 and for p>15, we obtain a lower bound on the maximum absolute value of these coefficients for sufficiently large n.
关键词	Borwein conjectures Positivity Multinomial Sieve
相关链接	[来源记录]
收录类别	SCI
语种	英语
学校署名	其他
资助项目	Austrian Science Fund (FWF)[SFB F50-06]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000618966000002
出版者	SPRINGER
ESI学科分类	MATHEMATICS
来源库	Web of Science
引用统计	被引频次[WOS]：1
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/221017
专题	理学院_数学系
作者单位	1.JKU, Res Inst Symbol Computat RISC, Linz, Austria 2.Southern Univ Sci & Technol SUSTECH, Dept Math, Shenzhen, Peoples R China
推荐引用方式 GB/T 7714	Goswami, Ankush,Pantangi, Venkata Raghu Tej. On sums of coefficients of polynomials related to the Borwein conjectures[J]. RAMANUJAN JOURNAL,2021,57(1).
APA	Goswami, Ankush,&Pantangi, Venkata Raghu Tej.(2021).On sums of coefficients of polynomials related to the Borwein conjectures.RAMANUJAN JOURNAL,57(1).
MLA	Goswami, Ankush,et al."On sums of coefficients of polynomials related to the Borwein conjectures".RAMANUJAN JOURNAL 57.1(2021).