发表所有数学领域最高质量的原创研究论文。

The journal Acta Mathematica is dedicated to publishing original research papers of the highest quality across all areas of mathematics.

《Acta Mathematica》期刊致力于发表所有数学领域内最高质量的原创研究论文。

Acta Mathematica

Let f be a germ of an analytic function at infinity that can be analytically continued along any path in the complex plane deprived of a finite set of points, f∈A(C¯\A), #A<∞. J. Nuttall has put forward the important relation between the maximal domain of f where the function has a single-valued branch and the domain of convergence of the diagonal Padé approximants for f. The Padé approximants, which are rational functions and thus single-valued, approximate a holomorphic branch of f in the domain of their convergence. At the same time most of their poles tend to the boundary of the domain of convergence and the support of their limiting distribution models the system of cuts that makes the function f single-valued. Nuttall has conjectured (and proved for many important special cases) that this system of cuts has minimal logarithmic capacity among all other systems converting the function f to a single-valued branch. Thus the domain of convergence corresponds to the maximal (in the sense of minimal boundary) domain of single-valued holomorphy for the analytic function f∈A(C¯\A). The complete proof of Nuttall's conjecture (even in a more general setting where the set A has logarithmic capacity 0) was obtained by H. Stahl. In this work, we derive strong asymptotics for the denominators of the diagonal Padé approximants for this problem in a rather general setting. We assume that A is a finite set of branch points of f which have the algebro-logarithmic character and which are placed in a generic position. The last restriction means that we exclude from our consideration some degenerated "constellations" of the branch points.

Alexander I. Aptekarev

Maxim L. Yattselev

Padé approximants for functions with branch points — strong asymptotics of Nuttall–Stahl polynomials

具有分支点的函数的多项式逼近——Nuttall-Stahl多项式的强渐近性

We prove estimates for the level of distribution of the Mobius function, von Mangoldt function, and divisor functions in squarefree progressions in the ring of polynomials over a finite field. Each level of distribution converges to $1$ as $q$ goes to $\infty$, and the power savings converges to square-root cancellation as $q$ goes to $\infty$. These results in fact apply to a more general class of functions, the factorization functions, that includes these three. The divisor estimates have applications to the moments of $L$-functions, and the von Mangoldt estimate to one-level densities.

Will Sawin

Square-root cancellation for sums of factorization functions over squarefree progressions in $\mathbb{F}_q[t]$

$\mathbb{F}_q[t]$ 中无平方因子的等差数列上的因式分解函数和的平方根抵消

2 ) Given a (possibly empty) list of objects L, for real numbers Ap, Bp 0 depending on some Lebesgue exponent p, the notation Ap L Bp or Bp L Ap signifies that Ap CBp for some constant C =C L,n,p 0 depending on the objects in the list, n and p.In addition, Ap ∼ L Bp is used to signify that Ap L Bp and Ap L Bp.( 4 ) In particular, Lee [19] proved that for positive-definite phases (1.4) holds for p 2(n+2)/n in all dimensions, extending the range in Theorem 1.1 when n is odd.( 7 ) The connection with Bochner-Riesz multipliers is made via the classical reduction of Carleson-Sjölin [10], [17], as discussed in the previous subsection.

Larry Guth

Jonathan Hickman

Marina Iliopoulou

Sharp estimates for oscillatory integral operators via polynomial partitioning

通过多项式分割对振荡积分算子的精确估计

Yaroslav Shitov

Counterexamples to Strassen’s direct sum conjecture

反例证明Strassen的直接和猜想不成立

We prove that for every non-negative integer $g$, there exists a bound on the number of ends of a complete, embedded minimal surface $M$ in $\mathbb{R}^3$ of genus $g$ and finite topology. This bound on the finite number of ends when $M$ has at least two ends implies that $M$ has finite stability index which is bounded by a constant that only depends on its genus.

William H. Meeks

Joaquín Pérez

Antonio Ros

Bounds on the topology and index of minimal surfaces

极小曲面的拓扑和指标的界

Jeremy Kahn

François Labourie

Mozes Shahar

Surface groups in uniform lattices of some semi-simple groups

某些半单群的均匀格中的表面群

James Gabe

Gábor Szabó

The dynamical Kirchberg–Phillips theorem

动力学Kirchberg–Phillips定理

Song Sun

Ruobing Zhang

&lt;span style="font-size: 11.0pt; line-height: 115%; font-family: 'Calibri','sans-serif'; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;"&gt;Collapsing geometry of hyperk&amp;auml;hler 4-manifolds and applications&lt;/span&gt;

超凯勒4-流形的塌缩几何及其应用

We discuss the dynamics of smooth diffeomorphisms of the disc with vanishing topological entropy which satisfy the mild dissipation property introduced in [CP]. In particular it contains the Henon maps with Jacobian up to 1/4. We prove that these systems are either (generalized) Morse Smale or infinitely renormalizable. In particular we prove for this class of diffeomorphisms a conjecture of Tresser: any diffeomorphism in the interface between the sets of systems with zero and positive entropy admits doubling cascades. This generalizes for these surface dynamics a well known consequence of Sharkovskii's theorem for interval maps.

Abbreviation	Acta Math.
Journal Impact	5.01
Quartiles(Global)	MATHEMATICS(Q1)

ISSN	0001-5962, 1871-2509
h-index	76
Top Journals	Yes

Publication Information	Publisher: Springer Netherlands，Publishing cycle: Quarterly，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 1944，Proportion of original research papers: 100.00%，Self Citation Rate:0.00%， Gold OA Rate: 96.00%
Average review cycle	网友分享经验：>12周，或约稿
Average recruitment ratio	网友分享经验：较易

Acta Mathematica

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Padé approximants for functions with branch points — strong asymptotics of Nuttall–Stahl polynomials

Square-root cancellation for sums of factorization functions over squarefree progressions in $\mathbb{F}_q[t]$

Sharp estimates for oscillatory integral operators via polynomial partitioning

Counterexamples to Strassen’s direct sum conjecture

Bounds on the topology and index of minimal surfaces

Square-root cancellation for sums of factorization functions over squarefree progressions in $\mathbb{F}_q[t]$

Surface groups in uniform lattices of some semi-simple groups

The dynamical Kirchberg–Phillips theorem

Mildly dissipative diffeomorphisms of the disk with zero entropy

Acta Mathematica

Journal Citation Format

A journal article with 1 author

A journal article with 2 authors

A journal article with 3 authors

A journal article with 5 or more authors

Books Citation Format

Thesis Citation Format

Web sites Citation Format

Patent Citation Format

Staying up late manually editing references? ivySCI automatically matches journals and helps you generate references with a single click.

Share Submission Experience

Padé approximants for functions with branch points — strong asymptotics of Nuttall–Stahl polynomials

Square-root cancellation for sums of factorization functions over squarefree progressions in $\mathbb{F}_q[t]$

Sharp estimates for oscillatory integral operators via polynomial partitioning

Counterexamples to Strassen’s direct sum conjecture

Bounds on the topology and index of minimal surfaces

Square-root cancellation for sums of factorization functions over squarefree progressions in $\mathbb{F}_q[t]$

Surface groups in uniform lattices of some semi-simple groups

The dynamical Kirchberg–Phillips theorem

Mildly dissipative diffeomorphisms&nbsp;of the disk with zero entropy

Mildly dissipative diffeomorphisms of the disk with zero entropy