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Bounds for the Tornheim double zeta function Tornheim双zeta函数的边界
Proceedings of the American Mathematical Society, Series B
Pub Date : 2023-02-02 DOI: 10.1090/bproc/142
Takashi Nakamura

In the present paper, we give bounds for the Tornheim double zeta function T ( s 1 , s 2 , s 3 ) T(s_1,s_2,s_3) when | t 1 | , | t 2 | , | t 3 | ≥ 1 lvert t_1 rvert , lvert t_2 rvert , lvert t_3 rvert ge 1 , | t 1 + t 2 | , | t 2 +

本文给出了Tornheim双zeta函数T(s1, s2, s3) T(s＿1,s＿2,s＿3)当| T 1 |， | T 2 |， | T 3 |≥1 lvert t＿1 rvert, lvert t＿2 rvert，lvert t＿3 rvertge 1， | t 1 + t 2 |， | t 2 + t 3 |， | t 3 + t 1 |≥1 lvert t＿1 + t＿2 rvert, lvert t＿2 + t＿3 rvert，lvert t＿3 + t＿1 rvertge 1和| t1 + t2 + t3 |≥1 lvert t＿1 + t2 + t3 rvertge 1 with σ 1， σ 2， σ 3 >−K sigma ＿1, sigma ＿2，sigma ＿3 > -K和σ 1 + σ 2， σ 2 + σ 3， σ 3 + σ 1 > 1−K sigma ＿1 + sigma ＿2, sigma ＿2 + sigma ＿3, sigma ＿3 + sigma ＿1 > 1-K，其中K K为正整数，由指数和的布尔甘边界所显示的Hurwitz zeta函数的边界。
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引用次数: 0
Sarnak’s conjecture for a class of rank-one subshifts 一类秩一子位移的Sarnak猜想
Proceedings of the American Mathematical Society, Series B
Pub Date : 2022-12-19 DOI: 10.1090/bproc/148
Mahmood Etedadialiabadi, Su Gao
Using techniques developed by Kanigowski, Lemańczyk, and Radziwiłł [Fund. Math. 255 (2021), pp. 309–336], we verify Sarnak’s conjecture for two classes of rank-one subshifts with unbounded cutting parameters. The first class of rank-one subshifts we consider is called almost complete congruency classes (accc), the definition of which is motivated by the main result of Foreman, Gao, Hill, Silva, and Weiss [Isr. J. Math., To appear], which implies that when a rank-one subshift carries a unique nonatomic invariant probability measure, it is accc if it is measure-theoretically isomorphic to an odometer. The second class we consider consists of Katok’s map and its generalizations.
使用Kanigowski、Lemańczyk和Radziwiłł开发的技术[基金]。数学。255 (2021)，pp. 309-336]，我们验证了Sarnak猜想的两类具有无界切割参数的一阶子位移。我们考虑的第一类排名第一的子移位被称为几乎完全同余类(accc)，其定义是由Foreman, Gao, Hill, Silva和Weiss [Isr]的主要结果激发的。j .数学。，这意味着当一个秩一子移携带一个唯一的非原子不变概率测度时，如果它在测度理论上同构于里程表，则它是可访问的。我们考虑的第二类包括Katok的地图及其概括。
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引用次数: 0
A 4-fold categorical equivalence 四重分类等价
Proceedings of the American Mathematical Society, Series B
Pub Date : 2022-11-30 DOI: 10.1090/bproc/178
Ray Maresca
In this note, we will illuminate some immediate consequences of work done by Reineke in [Algebr. Represent. Theory 16 (2013), no. 5. 1313–1314] that may prove to be useful in the study of elliptic curves. In particular, we will construct an isomorphism between the category of smooth projective curves with a category of quiver Grassmannians. We will use this to provide a 4-fold categorical equivalence between a category of quiver Grassmannians, smooth projective curves, compact Riemann surfaces, and fields of transcendence degree 1 over C mathbb {C} . We finish with noting that the category of elliptic curves is isomorphic to a category of quiver Grassmannians, whence providing an analytic group structure to a class of quiver Grassmannians.
在本说明中，我们将阐明赖内克在[Algebr. Represent. Theory 16 (2013)，no. 5. 1313-1314]中所做工作的一些直接后果，这些后果可能被证明对椭圆曲线研究有用。特别是，我们将在光滑投影曲线范畴与四分格拉斯曼范畴之间构建一个同构。我们将利用这一点，在quiver Grassmannians、光滑射影曲线、紧凑黎曼曲面和C mathbb {C} 上的超越度为1的域之间提供一个4折分类等价。最后，我们指出椭圆曲线范畴与四维格拉斯曼范畴同构，从而为四维格拉斯曼范畴提供了一个解析群结构。
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引用次数: 0
A modular construction of unramified 𝑝-extensions of ℚ(ℕ^{1/𝕡}) π (n ^{1/𝕡})的无分枝𝑝-extensions的模构造
Proceedings of the American Mathematical Society, Series B
Pub Date : 2022-10-31 DOI: 10.1090/bproc/141
Jaclyn Lang, Preston Wake

We show that for primes N , p ≥ 5 N, p geq 5 with N ≡ − 1 mod p N equiv -1 bmod p , the class number of Q ( N 1 / p ) mathbb {Q}(N^{1/p}) is divisible by p p . Our methods are via congruences between Eisenstein series and cusp forms. In particular, we show that when N ≡ − 1 mod p N equiv -1 bmod p , there is always a cusp form of weight

证明了对于素数N, p≥5n, p geq 5，且N≡-1 mod p N equiv -1 bmod p，则类数Q(N 1/p) mathbb Q{(N^}1/p{)可被p整除。我们的方法是通过爱森斯坦级数和尖形的同余。特别地，我们证明了当N≡−1模p N }equiv -1 bmod p时，总有一个权值2和阶数Γ 0(n2) Gamma ＿0(N^2)的尖点形式，其∑ell傅里叶系数等于p p以上的∑1 ell + 1模a撇，对于所有素数来说，都是ell。我们使用这种尖头形式的伽罗瓦表示来显式地构造Q(N 1/p) mathbb Q{(N^}1/p)的非分叉度- p{扩展。}
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引用次数: 0
Milnor operations and classifying spaces 米尔诺运算和分类空间
Proceedings of the American Mathematical Society, Series B
Pub Date : 2022-10-07 DOI: 10.1090/bproc/177
Masaki Kameko
We give an example of a nonzero odd degree element of the classifying space of a connected Lie group such that all higher Milnor operations vanish on it. It is a counterexample of a conjecture of Kono and Yagita [Trans. Amer. Math. Soc. 339 (1993), pp. 781–798].
我们给出了连通李群的分类空间的非零奇次元的一个例子，使得所有的高Milnor运算在其上都消失。它是Kono和Yagita猜想的反例[译]。阿米尔。数学。《社会法学》(1993)，第781-798页。
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引用次数: 0
Alternative proofs of Mandrekar’s theorem Mandrekar定理的其他证明
Proceedings of the American Mathematical Society, Series B
Pub Date : 2022-09-29 DOI: 10.1090/bproc/156
Linus Bergqvist
We present two alternative proofs of Mandrekar’s theorem, which states that an invariant subspace of the Hardy space on the bidisc is of Beurling type precisely when the shifts satisfy a doubly commuting condition [Proc. Amer. Math. Soc. 103 (1988), pp. 145–148]. The first proof uses properties of Toeplitz operators to derive a formula for the reproducing kernel of certain shift invariant subspaces, which can then be used to characterize them. The second proof relies on the reproducing property in order to show that the reproducing kernel at the origin must generate the entire shift invariant subspace.
本文给出了Mandrekar定理的两种替代证明，该定理表明，当位移满足双交换条件时，Hardy空间的不变子空间是Beurling型的。数学。《社会法学》(1988)，第145-148页。第一个证明利用Toeplitz算子的性质推导出了一个移不变子空间的再现核的公式，然后用它来表征它们。第二个证明依赖于再现性，以证明在原点处的再现核必须生成整个移位不变量子空间。
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引用次数: 0
Toeplitz separability, entanglement, and complete positivity using operator system duality 利用算子系统对偶性的Toeplitz可分性、纠缠性和完全正性
Proceedings of the American Mathematical Society, Series B
Pub Date : 2022-08-05 DOI: 10.1090/bproc/163
D. Farenick, Michelle McBurney

A new proof is presented of a theorem of L. Gurvits [LANL Unclassified Technical Report (2001), LAUR–01–2030], which states that the cone of positive block-Toeplitz matrices with matrix entries has no entangled elements. The proof of the Gurvits separation theorem is achieved by making use of the structure of the operator system dual of the operator system C ( S 1 ) ( n ) C(S^1)^{(n)} of n × n ntimes n Toeplitz matrices over the complex field, and by determining precisely the structure of the generators of the extremal rays of the positive cones of the operator systems C ( S 1 ) ( n ) ⊗ min B ( H

本文给出了L. Gurvits [LANL Unclassified Technical Report (2001)， lur - 01 - 2030]的一个定理的一个新的证明，该定理表明具有矩阵项的正块toeplitz矩阵的锥不存在纠缠元。利用算子系统C(s1) (n) C(S^1)^(n) (n × n) {}times n Toeplitz矩阵在复域上的算子系统对偶结构实现了Gurvits分离定理的证明，并通过精确地确定算子系统C(s1) (n)⊗min B(H) C(s1)^{(n)}otimes ＿ {text min{}}mathcal B{(}mathcal H{)和C(S)的正锥极值射线发生器的结构1) (n)⊗min B(H) C(S^1)＿}(n){}otimes ＿ {text min{}}mathcal B{(}mathcal H{)，H }mathcal H{是一个任意的希尔伯特空间C(s1) (n) C(s1)＿}(n){是C(s1) (n) C(s1)^(n)的算子系统对偶。当H }{}mathcal H具有无限维数时，我们的方法还提供了关于项来自B(H) {}mathcal B{(}mathcal H{)的正Toeplitz矩阵的一些新信息。特别地，我们证明了B(H) }mathcal B(mathcal H)上的正规正线性映射ψ {}psi在ψ (n)(x) {}psi ^(n){(x)}
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引用次数: 2
The Kac formula and Poincaré recurrence theorem in Riesz spaces Riesz空间中的Kac公式和poincarcars递归定理
Proceedings of the American Mathematical Society, Series B
Pub Date : 2022-07-25 DOI: 10.1090/bproc/152
Youssef Azouzi, M. B. Amor, Jonathan Homann, Marwa Masmoudi, B. Watson
Riesz space (non-pointwise) generalizations for iterative processes are given for the concepts of recurrence, first recurrence and conditional ergodicity. Riesz space conditional versions of the Poincaré Recurrence Theorem and the Kac formula are developed. Under mild assumptions, it is shown that every conditional expectation preserving process is conditionally ergodic with respect to the conditional expectation generated by the Cesàro mean associated with the iterates of the process. Applied to processes in L 1 ( Ω , A , μ ) L^1(Omega ,{mathcal A},mu ) , where μ mu is a probability measure, new conditional versions of the above theorems are obtained.
给出了迭代过程的递归、一递归和条件遍历概念的Riesz空间(非点态)推广。提出了黎兹空间条件版本的庞卡罗什递归定理和卡茨公式。在温和的假设下，证明了每个条件期望保持过程相对于与该过程的迭代相关的Cesàro均值生成的条件期望是有条件遍历的。应用于l1 (Ω， A， μ) L^1(Omega, {mathcal A, }mu)中的过程，其中μ mu是一个概率度量，得到了上述定理的新条件版本。
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引用次数: 1
Tower equivalence and Lusztig’s truncated Fourier transform 塔等效和Lusztig截断傅里叶变换
Proceedings of the American Mathematical Society, Series B
Pub Date : 2022-07-18 DOI: 10.1090/bproc/167
J. Michel
If f f denotes the truncated Lusztig Fourier transform, we show that the image by f f of the normalized characteristic function of a Coxeter element is the alternate sum of the exterior powers of the reflection representation, and that any class function is tower equivalent to its image by f f . In particular this gives a proof of the results of Chapuy and Douvropoulos on “Coxeter factorizations with generalized Jucys-Murphy weights and matrix tree theorems for reflection groups” for irreducible spetsial reflection groups, based on Deligne-Lusztig combinatorics.
如果f f表示截断的Lusztig傅里叶变换，我们证明了Coxeter元素的归一化特征函数的f的像是反射表示的外幂的交替和，并且任何类函数都等于它的f的像。特别地，基于delig - lusztig组合给出了Chapuy和Douvropoulos关于不可约特殊反射群的“广义juys - murphy权的Coxeter分解和反射群的矩阵树定理”的证明。
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引用次数: 3
Remarks on the Navier-Stokes equations in space dimension 𝑛≥3 关于空间维度𝑛≥3的Navier-Stokes方程的注释
Proceedings of the American Mathematical Society, Series B
Pub Date : 2022-07-12 DOI: 10.1090/bproc/135
Jishan Fan, T. Ozawa

In this paper, we prove some new L p L^p -estimates of the velocity by the technique of L p L^p -energy method.

本文用lpl ^p能量法证明了一些新的lpl ^p速度估计。
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引用次数: 0
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