波兰科学研究院数学研究所
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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...

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