scholarly journals Relative regular Riemann–Hilbert correspondence ( Proc. London Math. Soc . (3) 122 (2021) 434–457)

2021 ◽  
Author(s):  
Luisa Fiorot ◽  
Teresa Monteiro Fernandes ◽  
Claude Sabbah
Keyword(s):  
London Math

On the existence of ergodic automorphisms in ergodic ℤd-actions on compact groups

2009 ◽  
Vol 30 (6) ◽  
pp. 1803-1816 ◽  
Author(s):  
C. R. E. RAJA
Keyword(s):  
London Math ◽  
Abelian Groups ◽  
Chain Condition ◽  
Compact Groups ◽  
Finitely Generated ◽  
Finitely Generated Group ◽  
Metrizable Group ◽  
Compact Abelian Groups ◽  
Descending Chain Condition

AbstractLet K be a compact metrizable group and Γ be a finitely generated group of commuting automorphisms of K. We show that ergodicity of Γ implies Γ contains ergodic automorphisms if center of the action, Z(Γ)={α∈Aut(K)∣α commutes with elements of Γ} has descending chain condition. To explain that the condition on the center of the action is not restrictive, we discuss certain abelian groups which, in particular, provide new proofs to the theorems of Berend [Ergodic semigroups of epimorphisms. Trans. Amer. Math. Soc.289(1) (1985), 393–407] and Schmidt [Automorphisms of compact abelian groups and affine varieties. Proc. London Math. Soc. (3) 61 (1990), 480–496].

scholarly journals A Note on Rényi's ‘Record’ Problem and Engel's Series

2018 ◽  
Vol 61 (2) ◽  
pp. 363-369 ◽  
Author(s):  
Lulu Fang ◽  
Min Wu
Keyword(s):  
Number Theory ◽  
Large Deviations ◽  
Markov Processes ◽  
Classical Limit ◽  
Limit Theorems ◽  
London Math ◽  
Law Of Large Numbers ◽  
Record Times ◽  
Iterated Logarithm ◽  
Large Numbers

AbstractIn 1973, Williams [D. Williams, On Rényi's ‘record’ problem and Engel's series, Bull. London Math. Soc.5 (1973), 235–237] introduced two interesting discrete Markov processes, namely C-processes and A-processes, which are related to record times in statistics and Engel's series in number theory respectively. Moreover, he showed that these two processes share the same classical limit theorems, such as the law of large numbers, central limit theorem and law of the iterated logarithm. In this paper, we consider the large deviations for these two Markov processes, which indicate that there is a difference between C-processes and A-processes in the context of large deviations.

Universally Koszul and initially Koszul properties of Orlik–Solomon algebras

2019 ◽  
Vol 19 (11) ◽  
pp. 2050218
Author(s):  
Phong Dinh Thieu
Keyword(s):  
London Math ◽  
Exterior Algebra ◽  
Hyperplane Arrangements ◽  
Koszul Algebras ◽  
Graded Algebra ◽  
Standing Question

Let [Formula: see text] be a field with [Formula: see text] and [Formula: see text] an exterior algebra over [Formula: see text] with a standard grading [Formula: see text]. Let [Formula: see text] be a graded algebra, where [Formula: see text] is a graded ideal in [Formula: see text]. In this paper, we study universally Koszul and initially Koszul properties of [Formula: see text] and find classes of ideals [Formula: see text] which characterize such properties of [Formula: see text]. As applications, we classify arrangements whose Orlik–Solomon algebras are universally Koszul or initially Koszul. These results are related to a long-standing question of Shelton–Yuzvinsky [B. Shelton and S. Yuzvinsky, Koszul algebras from graphs and hyperplane arrangements, J. London Math. Soc. 56 (1997) 477–490].

scholarly journals IDENTITIES OF THE ROGERS–RAMANUJAN–SLATER TYPE

2007 ◽  
Vol 03 (02) ◽  
pp. 293-323 ◽  
Author(s):  
ANDREW V. SILLS
Keyword(s):  
Difference Equations ◽  
London Math ◽  
Slater Type ◽  
Bailey Pairs ◽  
Combinatorial Interpretations

It is shown that (two-variable generalizations of) more than half of Slater's list of 130 Rogers–Ramanujan identities (L. J. Slater, Further identities of the Rogers–Ramanujan type, Proc. London Math Soc. (2)54 (1952) 147–167) can be easily derived using just three multiparameter Bailey pairs and their associated q-difference equations. As a bonus, new Rogers–Ramanujan type identities are found along with natural combinatorial interpretations for many of these identities.

scholarly journals VIII. On the diameters of plane cubics. preliminary notice

1887 ◽  
Vol 42 (251-257) ◽  
pp. 334-335
Keyword(s):  
London Math

I showed some time back (‘London Math. Soc. Proc.,’ vol. 10, pp. 184-5) that the Newtonian diameters of a plane cubic ( u ) envelope a conic, called hereinafter its “centroid,” the equation of which, if in the system of co-ordinates chosen the line at infinity be

Relative and Tate homology with respect to semidualizing modules

2014 ◽  
Vol 13 (08) ◽  
pp. 1450058 ◽  
Author(s):  
Zhenxing Di ◽  
Xiaoxiang Zhang ◽  
Zhongkui Liu ◽  
Jianlong Chen
Keyword(s):  
Exact Sequence ◽  
London Math ◽  
Projective Dimension ◽  
Relative Cohomology ◽  
Relative Homology ◽  
Semidualizing Module ◽  
Coherent Ring ◽  
Semidualizing Modules ◽  
Tate Homology ◽  
Dualizing Module

We introduce and investigate in this paper a kind of Tate homology of modules over a commutative coherent ring based on Tate ℱC-resolutions, where C is a semidualizing module. We show firstly that the class of modules admitting a Tate ℱC-resolution is equal to the class of modules of finite 𝒢(ℱC)-projective dimension. Then an Avramov–Martsinkovsky type exact sequence is constructed to connect such Tate homology functors and relative homology functors. Finally, motivated by the idea of Sather–Wagstaff et al. [Comparison of relative cohomology theories with respect to semidualizing modules, Math. Z. 264 (2010) 571–600], we establish a balance result for such Tate homology over a Cohen–Macaulay ring with a dualizing module by using a good conclusion provided in [E. E. Enochs, S. E. Estrada and A. C. Iacob, Balance with unbounded complexes, Bull. London Math. Soc. 44 (2012) 439–442].

scholarly journals Corrigendum

1972 ◽  
Vol 71 (2) ◽  
pp. 431-431
Keyword(s):  
Special Reference ◽  
Elliptic Curves ◽  
London Math ◽  
Diophantine Equations

J. W. S. Cassels, A note on the division values of ℘(u).Monsieur Y. Hellegouarch has pointed out to me that the inequality (131) of my paper “A note on the division values of ℘ (u)” (Proc. Cambridge Phil. Soc.45 (1949), 169–172) does not follow from the argument hinted there and is almost certainly incorrect. All the argument shows is that the rather weaker estimate in (132) holds for m = pk as well as for m = 2pk.The erroneous claim is reproduced in my report “Diophantine equations with special reference to elliptic curves” (J. London Math. Soc.41 (1966), 193–291) in expression (17.14) on page 247.

OMEGA THEOREMS FOR $\frac{L'}{L}(1, \chi_D)$

2013 ◽  
Vol 09 (03) ◽  
pp. 561-581 ◽  
Author(s):  
M. MOURTADA ◽  
V. KUMAR MURTY
Keyword(s):  
Classical Result ◽  
London Math ◽  
Quadratic Field ◽  
Analogous Result ◽  
Logarithmic Derivative ◽  
Dirichlet Character ◽  
Derivative Formula ◽  
Derivatives Of ◽  
Logarithmic Derivatives

A classical result of Chowla [Improvement of a theorem of Linnik and Walfisz, Proc. London Math. Soc. (2) 50 (1949) 423–429 and The Collected Papers of Sarvadaman Chowla, Vol. 2 (Centre de Recherches Mathematiques, 1999), pp. 696–702] states that for infinitely many fundamental discriminants D we have [Formula: see text] where χD is the quadratic Dirichlet character of conductor D. In this paper, we prove an analogous result for the logarithmic derivative [Formula: see text], and investigate the growth of the logarithmic derivatives of real Dirichlet L-functions. We show that there are infinitely many fundamental discriminants D (both positive and negative) such that [Formula: see text] and infinitely many fundamental discriminants 0 < D such that [Formula: see text] In particular, we show that the Euler–Kronecker constant γK of a quadratic field K satisfies γK = Ω( log log |dK|). We get sharper results assuming the GRH. Moreover, we evaluate the moments of [Formula: see text].

scholarly journals WHEN LATTICE HOMOMORPHISMS OF ARCHIMEDEAN VECTOR LATTICES ARE RIESZ HOMOMORPHISMS

2009 ◽  
Vol 87 (2) ◽  
pp. 263-273 ◽  
Author(s):  
MOHAMED ALI TOUMI
Keyword(s):  
London Math ◽  
Lattice Homomorphism ◽  
Vector Lattices ◽  
Lattice Homomorphisms ◽  
Orthogonal Systems

AbstractLet A, B be Archimedean vector lattices and let (ui)i∈I, (vi)i∈I be maximal orthogonal systems of A and B, respectively. In this paper, we prove that if T is a lattice homomorphism from A into B such that $T\left ( \lambda u_{i}\right ) =\lambda v_{i}$ for each λ∈ℝ+ and i∈I, then T is linear. This generalizes earlier results of Ercan and Wickstead (Math. Nachr279 (9–10) (2006), 1024–1027), Lochan and Strauss (J. London Math. Soc. (2) 25 (1982), 379–384), Mena and Roth (Proc. Amer. Math. Soc.71 (1978), 11–12) and Thanh (Ann. Univ. Sci. Budapest. Eotvos Sect. Math.34 (1992), 167–171).

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