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Colloquium Mathematicum最新文献

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Additive bases of $C_3oplus C_{3q}$ $C_3oplus C_｛3q｝的加性基$
IF 0.4 4区 数学
Colloquium Mathematicum Pub Date : 2021-07-14 DOI: 10.4064/cm8515-6-2021
Yongke Qu, Yuanlin Li
{"title":"Additive bases of $C_3oplus C_{3q}$","authors":"Yongke Qu, Yuanlin Li","doi":"10.4064/cm8515-6-2021","DOIUrl":"https://doi.org/10.4064/cm8515-6-2021","url":null,"abstract":"Let G be a finite abelian group and p be the smallest prime dividing |G|. Let S be a sequence over G. We say that S is regular if for every proper subgroup H ( G, S contains at most |H | − 1 terms from H . Let c0(G) be the smallest integer t such that every regular sequence S over G of length |S| ≥ t forms an additive basis of G, i.e., ∑ (S) = G. The invariant c0(G) was first studied by Olson and Peng in 1980’s, and since then it has been determined for all finite abelian groups except for the groups with rank 2 and a few groups of rank 3 or 4 with order less than 10. In this paper, we focus on the remaining case concerning groups of rank 2. It was conjectured by the first author and Han (Int. J. Number Theory 13 (2017) 2453-2459) that c0(G) = pn+2p− 3 where G = Cp ⊕ Cpn with n ≥ 3. We confirm the conjecture for the case when p = 3 and n = q (≥ 5) is a prime number.","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49301244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On a conjecture of Zhuang and Gao 关于庄、高的一个猜想
IF 0.4 4区 数学
Colloquium Mathematicum Pub Date : 2021-07-14 DOI: 10.4064/cm8685-2-2022
Yongke Qu, Yuanlin Li
{"title":"On a conjecture of Zhuang and Gao","authors":"Yongke Qu, Yuanlin Li","doi":"10.4064/cm8685-2-2022","DOIUrl":"https://doi.org/10.4064/cm8685-2-2022","url":null,"abstract":"Let G be a multiplicatively written finite group. We denote by E(G) the smallest integer t such that every sequence of t elements in G contains a product-one subsequence of length |G|. In 1961, Erdős, Ginzburg and Ziv proved that E(G) ≤ 2|G|−1 for every finite ablian group G and this result is known as the Erdős-Ginzburg-Ziv Theorem. In 2005, Zhuang and Gao conjectured that E(G) = d(G) + |G|, where d(G) is the small Davenport constant. In this paper, we confirm the conjecture for the case when G = 〈x, y|x = y = 1, xyx = y〉, where p is the smallest prime divisor of |G| and gcd(p(r − 1),m) = 1.","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48460074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Bump conditions and two-weight inequalities for commutators of fractional integrals 分数阶积分对易子的碰撞条件和双权不等式
IF 0.4 4区 数学
Colloquium Mathematicum Pub Date : 2021-07-07 DOI: 10.4064/cm8703-4-2022
Yongming Wen, Huo-xiong Wu
{"title":"Bump conditions and two-weight inequalities for commutators of fractional integrals","authors":"Yongming Wen, Huo-xiong Wu","doi":"10.4064/cm8703-4-2022","DOIUrl":"https://doi.org/10.4064/cm8703-4-2022","url":null,"abstract":"This paper gives new two-weight bump conditions for the sparse operators related to iterated commutators of fractional integrals. As applications, the two-weight bounds for iterated commutators of fractional integrals under more general bump conditions are obtained. Meanwhile, the necessity of two-weight bump conditions as well as the converse of Bloom type estimates for iterated commutators of fractional integrals are also given.","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44459512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Powerfree sums of proper divisors 固有因子的无幂和
IF 0.4 4区 数学
Colloquium Mathematicum Pub Date : 2021-06-28 DOI: 10.4064/cm8616-10-2021
P. Pollack, A. Roy
{"title":"Powerfree sums of proper divisors","authors":"P. Pollack, A. Roy","doi":"10.4064/cm8616-10-2021","DOIUrl":"https://doi.org/10.4064/cm8616-10-2021","url":null,"abstract":". Let s ( n ) := (cid:80) d | n,d<n d denote the sum of the proper divisors of n . It is natural to conjecture that for each integer k ≥ 2 , the equivalence n is k th powerfree ⇐⇒ s ( n ) is k th powerfree holds almost always (meaning, on a set of asymptotic density 1 ). We prove this for k ≥ 4 .","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46099791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A note on $G$-operators of order $2$ 关于$G$-阶为$2的算子的一个注记$
IF 0.4 4区 数学
Colloquium Mathematicum Pub Date : 2021-06-10 DOI: 10.4064/cm8600-3-2022
S. Fischler, T. Rivoal
{"title":"A note on $G$-operators of order $2$","authors":"S. Fischler, T. Rivoal","doi":"10.4064/cm8600-3-2022","DOIUrl":"https://doi.org/10.4064/cm8600-3-2022","url":null,"abstract":"It is known that G-functions solutions of a linear differential equation of order 1 with coefficients in Q(z) are algebraic (of a very precise form). No general result is known when the order is 2. In this paper, we determine the form of a G-function solution of an inhomogeneous equation of order 1 with coefficients in Q(z), as well as that of a G-function f of differential order 2 over Q(z) and such that f and f ′ are algebraically dependent over C(z). Our results apply more generally to holonomic Nilsson-Gevrey arithmetic series of order 0 that encompass G-functions.","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46325998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Bounds for moments of quadratic Dirichlet $L$-functions of prime-related moduli 二次Dirichlet $L$-素数相关模函数矩的界
IF 0.4 4区 数学
Colloquium Mathematicum Pub Date : 2021-05-08 DOI: 10.4064/cm8650-1-2022
Peng Gao, Liangyi Zhao
{"title":"Bounds for moments of quadratic Dirichlet $L$-functions of prime-related moduli","authors":"Peng Gao, Liangyi Zhao","doi":"10.4064/cm8650-1-2022","DOIUrl":"https://doi.org/10.4064/cm8650-1-2022","url":null,"abstract":". In this paper, we study the k -th moment of central values of the family of quadratic Dirichlet L -functions of moduli 8 p , with p ranging over odd primes. Assuming the truth of the generalized Riemann hypothesis, we establish sharp upper and lower bounds for the k -th power moment of these L -values for all real k ≥ 0.","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44228415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
On dense subsets in spaces of metrics 关于度量空间中的稠密子集
IF 0.4 4区 数学
Colloquium Mathematicum Pub Date : 2021-04-26 DOI: 10.4064/cm8580-9-2021
Yoshito Ishiki
{"title":"On dense subsets in spaces of metrics","authors":"Yoshito Ishiki","doi":"10.4064/cm8580-9-2021","DOIUrl":"https://doi.org/10.4064/cm8580-9-2021","url":null,"abstract":"In spaces of metrics, we investigate topological distributions of the doubling property, the uniform disconnectedness, and the uniform perfectness, which are the quasi-symmetrically invariant properties appearing in the David--Semmes theorem. We show that the set of all doubling metrics and the set of all uniformly disconnected metrics are dense in spaces of metrics on finite-dimensional and zero-dimensional compact metrizable spaces, respectively. Conversely, this denseness of the sets implies the finite-dimensionality, zero-dimensionality, and the compactness of metrizable spaces. We also determine the topological distribution of the set of all uniformly perfect metrics in the space of metrics on the Cantor set.","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43096608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Complementations in $C(K,X)$ and $ell _infty (X)$ $C(K,X)$和中的补充 $ell _infty (X)$
IF 0.4 4区 数学
Colloquium Mathematicum Pub Date : 2021-04-14 DOI: 10.4064/cm8868-10-2022
Leandro Candido
{"title":"Complementations in $C(K,X)$ and $ell _infty (X)$","authors":"Leandro Candido","doi":"10.4064/cm8868-10-2022","DOIUrl":"https://doi.org/10.4064/cm8868-10-2022","url":null,"abstract":"We investigate the geometry of $C(K,X)$ and $ell_{infty}(X)$ spaces through complemented subspaces of the form $left(bigoplus_{iin varGamma}X_iright)_{c_0}$. Concerning the geometry of $C(K,X)$ spaces we extend some results of D. Alspach and E. M. Galego from cite{AlspachGalego}. On $ell_{infty}$-sums of Banach spaces we prove that if $ell_{infty}(X)$ has a complemented subspace isomorphic to $c_0(Y)$, then, for some $n in mathbb{N}$, $X^n$ has a subspace isomorphic to $c_0(Y)$. We further prove the following: \u0000(1) If $C(K)sim c_0(C(K))$ and $C(L)sim c_0(C(L))$ and $ell_{infty}(C(K))sim ell_{infty}(C(L))$, then $K$ and $L$ have the same cardinality. \u0000(2) If $K_1$ and $K_2$ are infinite metric compacta, then $ell_{infty}(C(K_1))sim ell_{infty}(C(K_2))$ if and only if $C(K_1)$ is isomorphic to $C(K_2)$.","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41882649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Elliptic curves with exceptionally large analytic order of the Tate–Shafarevich groups Tate-Shafarevich群的特别大解析阶的椭圆曲线
IF 0.4 4区 数学
Colloquium Mathematicum Pub Date : 2021-03-19 DOI: 10.4064/CM8008-9-2020
A. Dkabrowski, L. Szymaszkiewicz
{"title":"Elliptic curves with exceptionally large analytic order of the Tate–Shafarevich groups","authors":"A. Dkabrowski, L. Szymaszkiewicz","doi":"10.4064/CM8008-9-2020","DOIUrl":"https://doi.org/10.4064/CM8008-9-2020","url":null,"abstract":"We exhibit $88$ examples of rank zero elliptic curves over the rationals with $|sza(E)| > 63408^2$, which was the largest previously known value for any explicit curve. Our record is an elliptic curve $E$ with $|sza(E)| = 1029212^2 = 2^4cdot 79^2 cdot 3257^2$. We can use deep results by Kolyvagin, Kato, Skinner-Urban and Skinner to prove that, in some cases, these orders are the true orders of $sza$. For instance, $410536^2$ is the true order of $sza(E)$ for $E= E_4(21,-233)$ from the table in section 2.3.","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46148455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
One-relator Sasakian groups 一个亲戚佐佐木集团
IF 0.4 4区 数学
Colloquium Mathematicum Pub Date : 2021-01-26 DOI: 10.4064/CM8521-3-2021
I. Biswas, Mahan Mj
{"title":"One-relator Sasakian groups","authors":"I. Biswas, Mahan Mj","doi":"10.4064/CM8521-3-2021","DOIUrl":"https://doi.org/10.4064/CM8521-3-2021","url":null,"abstract":"We prove that any one-relator group $G$ is the fundamental group of a compact Sasakian manifold if and only if $G$ is either finite cyclic or isomorphic to the fundamental group of a compact Riemann surface of genus g > 0 with at most one orbifold point of order $n geq 1$. We also classify all groups of deficiency at least two that are also the fundamental group of some compact Sasakian manifold.","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48612998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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