作者：Zdeněk Skalák 来源：[J].Annales Polonici Mathematici(IF 0.306), 2019, Vol.122, pp.193-199IMPAS 摘要：We show that if $u$ is a solution of the Navier–Stokes equations in the whole three-dimensional space and $\partial _3 u \in L^p(0,T;L^q(\mathbb {R}^3))$, $T \gt 0$, where $2/p+3/q=1+3/q$ and $q \in (3,10/3]$, then $u$ is regular on $(0,T]$.
 作者：Brandon Williams 来源：[J].Acta Arithmetica(IF 0.472), 2019, Vol.189, pp.347-365IMPAS 摘要：We prove that the generating function of overpartition $M2$-rank differences is, up to coefficient signs, a component of the vector-valued mock Eisenstein series attached to a certain quadratic form. We use this to compute analogs of the class number relations for $M2$-rank ...
 作者：Zhenchao Ge , Thái Hoàng Lê 来源：[J].Acta Arithmetica(IF 0.472), 2019, Vol.189, pp.381-390IMPAS 摘要：We generalize an argument of Wirsing to vector spaces over finite fields, giving a quantitative bound for the size of the sumset of an arbitrary set $A$ and a basis of the space. Then we use it to give a simpler proof of a result of Sanders on the existence of subspaces in the di...
 作者：Mirjana Milijević 来源：[J].Annales Polonici Mathematici(IF 0.306), 2019, Vol.122, pp.181-192IMPAS 摘要：We examine statistical hypersurfaces with shape operators having one or two constant eigenvalues, and establish the relation between the eigenvalues and the constant holomorphic sectional curvature of ambient manifolds.
 作者：Tomohiro Ooto 来源：[J].Acta Arithmetica(IF 0.472), 2019, Vol.189, pp.179-189IMPAS 摘要：As an analogue of Mahler’s classification for real numbers, Bundschuh introduced a classification for Laurent series over a finite field, divided into $A,S,T,U$-numbers. It is known that each of the sets of $A,S,U$-numbers is nonempty. On the other hand, the existence of $T$...
 作者：Chung-Chuan Chen , Kui-Yo Chen , Serap Öztop ... 来源：[J].Annales Polonici Mathematici(IF 0.306), 2019, Vol.122, pp.129-142IMPAS 摘要：Let $G$ be a locally compact group, and let $w$ be a weight on $G$. Let $\varPhi$ be a Young function. We give some characterizations for translation operators to be topologically transitive and chaotic on the weighted Orlicz space $L_w^\varPhi (G)$. In particular, transitivity ...
 作者：Benjamin Hutz , Michael Stoll 来源：[J].Acta Arithmetica(IF 0.472), 2019, Vol.189, pp.283-308IMPAS 摘要：We develop an algorithm that determines, for a given squarefreebinary form $F$ with real coefficients, a smallest representativeof its orbit under $\operatorname{SL}(2,\mathbb Z)$, either with respect to the Euclideannorm or with respect to the maximum norm of the coefficient vec...
 作者：SoYoung Choi , Bo-Hae Im 来源：[J].Acta Arithmetica(IF 0.472), 2019, Vol.190, pp.57-74IMPAS 摘要：We prove that certain infinitely many weakly holomorphic modular forms for $\Gamma_0(2)$ have all zeros on a part of a certain geodesic but not on the boundary of the fundamental domain $\mathfrak{F}$ of $\Gamma_0 (2)$, and prove that the zeros of one of these forms interlace wit...
 作者：Li-Xia Dai , Hao Pan 来源：[J].Acta Arithmetica(IF 0.472), 2019, Vol.189, pp.147-163IMPAS 摘要：We prove several extensions of the Erdős–Fuchs theorem. For example, for two subsets $A=\{a_1,a_2,\ldots\}$ and $B=\{b_1,b_2,\ldots\}$ of ${\mathbb N}$, if$$a_i-b_i=o(a_i^{1/4})$$as $i\to \infty$, then$$|\{(a,b): a\in A,\, b\in B,\, a+b\leq n\}|=cn+o(n^{1/4})$$is impossible ...
 作者：Biswajyoti Saha , Jyoti Sengupta 来源：[J].Acta Arithmetica(IF 0.472), 2019, Vol.189, pp.165-178IMPAS 摘要：We address the problem of determining a ${\bf GL}(2)$ Maass cusp form (of weight zero) from the central values of the Rankin–Selberg $L$-functions $L(1/2,f\otimes u_j)$ for infinitely many primes $p$ and all the normalised Maass cusp forms $u_j$ which are newforms for \$\varG...