The main result of this paper is to give that if b∈Lip⁡(ℝn), hj∈BMO⁡(ℝn), j=1,…,k, k∈ℤ+ and w∈Ap, 1

In this paper, we show that, for topological dynamical systems with a dense set (in the weak topology) of periodic measures, a typical (in Baire’s sense) invariant measure has, for each q>0, zero lower q-generalized fractal dimension. This implies, in particular, that a typical invariant measure has zero upper Hausdorff dimension and zero lower rate of recurrence. Of special interest is the full-shift

The theory of R. Crowell on derived modules is approached within the theory of non-commutative differential modules. We also seek analogies to the theory of cotangent complex from differentials in the commutative ring setting. Finally, we give examples motivated from the theory of Galois coverings of curves.

We explicitly prove the quantum modularity of partial theta series with even or odd periodic coefficients. As an application, we show that the Kontsevich–Zagier series Ft⁢(q) which matches (at a root of unity) the colored Jones polynomial for the family of torus knots T⁢(3,2t), t≥2, is a weight 32 quantum modular form. This generalizes Zagier’s result on the quantum modularity for the “strange” series

In this paper, we consider a finite-dimensional vector space 𝒫 over the Galois field GF⁡(p), with p being an odd prime, and the family ℬkx of all k-sets of elements of 𝒫 summing up to a given element x. The main result of the paper is the characterization, for x=0, of the permutations of 𝒫 inducing permutations of ℬk0 as the invertible linear mappings of the vector space 𝒫 if p does not divide

We study the Diophantine equations obtained by equating a polynomial and the factorial function, and prove the finiteness of integer solutions under certain conditions. For example, we show that there exist only finitely many l such that l! is represented by NA⁢(x), where NA is a norm form constructed from the field norm of a field extension K/𝐐. We also deal with the equation NA⁢(x)=l!S, where l

Let X and Y be pathwise connected and paracompact Hausdorff spaces equipped with free involutions T:X→X and S:Y→Y, respectively. Suppose that there exists a sequence

The spectrum of the Laplacian operator on the positive theta line bundle over the quasi-torus reduces to eigenvalues π⁢ℓ, ℓ=0,1,…, which are called Landau levels. This paper discusses the coherent state transform for each eigenspace associated with a Landau level. We construct a unitary transform valid for each eigenspace. A concrete form of the inverse formula for the proposed transform is also obtained

In this paper we show that how the representation theory of subcategories (of the category of modules over an Artin algebra) can be connected to the representation theory of all modules over some algebra. The subcategories dealing with are some certain subcategories of the morphism categories (including submodule categories studied recently by Ringel and Schmidmeier) and of the Gorenstein projective

In this paper, we prove a genuine analogue of the Wiener Tauberian theorem for Lp,1⁢(G) (1≤p<2), with G=SL⁢(2,ℝ).

Let Gn denote either the group SO⁢(2⁢n+1,F) or Sp⁢(2⁢n,F) over a non-archimedean local field of characteristic different than two. We study parabolically induced representations of the form 〈Δ〉⋊σ, where 〈Δ〉 denotes the Zelevinsky segment representation of the general linear group attached to the segment Δ, and σ denotes a discrete series representation of Gn. We determine the composition series of

Journal Name: Forum Mathematicum Volume: 33 Issue: 1 Pages: i-iv

Let 𝑀 be a connected compact PL 4-manifold with boundary. In this article, we give several lower bounds for regular genus and gem-complexity of the manifold 𝑀. In particular, we prove that if 𝑀 is a connected compact 4-manifold with ℎ boundary components, then its gem-complexity k⁢(M) satisfies the inequalities k⁢(M)≥3⁢χ⁢(M)+7⁢m+7⁢h-10 and k⁢(M)≥k⁢(∂⁡M)+3⁢χ⁢(M)+4⁢m+6⁢h-9, and its regular genus G⁢(M)

In this paper, our first goal is to rigorously define a Lévy process pinned at random time. Our second task is to establish the Markov property with respect to its completed natural filtration and thus with respect to the usual augmentation of the latter. The resulting conclusion is the right-continuity of completed natural filtration. Certain examples of such process are considered.

Let C be a complex algebraic curve uniformized by a Fuchsian group Γ. In the first part of this paper we identify the automorphism group of the solenoid associated with Γ with the Belyaev completion of its commensurator Comm⁢(Γ) and we use this identification to show that the isomorphism class of this completion is an invariant of the natural Galois action of Gal⁢(ℂ/ℚ) on algebraic curves. In turn

Let Y be a smooth del Pezzo surface of degree 3 polarized by a very ample divisor that is not proportional to the anticanonical one. Then the affine cone over Y is flexible in codimension one. Equivalently, such a cone has an open subset with an infinitely transitive action of the special automorphism group on it.

This paper studies the Prasad conjecture for the special orthogonal group SO3,3. Then we use the local theta correspondence between Sp4 and O⁢(V) to study the Sp4-distinction problems over a quadratic field extension E/F and dim⁡V=4 or 6. Thus we can verify the Prasad conjecture for a square-integrable representation of Sp4⁢(E).

In this paper we study smooth orientation-preserving free actions of the cyclic group ℤ/m on a class of (n-1)-connected 2⁢n-manifolds, ♯⁡♯⁡g⁢(Sn×Sn)Σ, where Σ is a homotopy 2⁢n-sphere. When n=2, we obtain a classification up to topological conjugation. When n=3, we obtain a classification up to smooth conjugation. When n≥4, we obtain a classification up to smooth conjugation when the prime factors

In this paper, we study hybrid subconvexity bounds for class group L-functions associated to quadratic extensions K/ℚ (real or imaginary). Our proof relies on relating the class group L-functions to Eisenstein series evaluated at Heegner points using formulas due to Hecke. The main technical contribution is the uniform sup norm bound for Eisenstein series E⁢(z,1/2+i⁢t)≪εy1/2⁢(|t|+1)1/3+ε, y≫1, extending

Journal Name: Forum Mathematicum Volume: 32 Issue: 6 Pages: i-iv

We classify commutative algebraic monoid structures on normal affine surfaces over an algebraically closed field of characteristic zero. The answer is given in two languages: comultiplications and Cox coordinates. The result follows from a more general classification of commutative monoid structures of rank 0, n-1 or 𝑛 on a normal affine variety of dimension 𝑛.

We establish explicit Ichino’s formulae for the central values of the triple product L-functions with emphasis on the calculations for the real place. The key ingredient for our computations is Proposition which generalizes a result in [P. Michel and A. Venkatesh, The subconvexity problem for GL2, Publ. Math. Inst. Hautes Études Sci. 111 2010, 171–271]. As an application we prove the optimal upper

We develop a version of Ekedahl’s geometric sieve for integral quadratic forms of rank at least five. As one ranges over the zeros of such quadratic forms, we use the sieve to compute the density of coprime values of polynomials, and furthermore, to address a question about local solubility in families of varieties parameterised by the zeros.

Let ℛ be a finite valuation ring of order qr. In this paper, we prove that for any quadratic polynomial f⁢(x,y,z)∈ℛ⁢[x,y,z] that is of the form a⁢x⁢y+R⁢(x)+S⁢(y)+T⁢(z) for some one-variable polynomials R,S,T, we have

We consider iterated integrals of log⁡ζ⁢(s) on certain vertical and horizontal lines. Here, the function ζ⁢(s) is the Riemann zeta-function. It is a well-known open problem whether or not the values of the Riemann zeta-function on the critical line are dense in the complex plane. In this paper, we give a result for the denseness of the values of the iterated integrals on the horizontal lines. By using

Moderate deviation principles (MDPs) for random walks on covering graphs with groups of polynomial volume growth are discussed in a geometric point of view. They deal with any intermediate spatial scalings between those of laws of large numbers and those of central limit theorems. The corresponding rate functions are given by quadratic forms determined by the Albanese metric associated with the given

We extend the definition of order zero maps to the setting of pro-C*-algebras and generalize structure theorems of order zero maps between C*-algebras to strongly bounded order zero maps between pro-C∗-algebras. An application to tensor products is included.

We prove a result that enables us to calculate the rational homotopy of a wide class of spaces by the theory of minimal models.

We study decompositions of length functions on integral domains as sums of length functions constructed from overrings. We find a standard representation when the integral domain admits a Jaffard family, when it is Noetherian and when it is a Prüfer domains such that every ideal has only finitely many minimal primes. We also show that there is a natural bijective correspondence between singular length

The twin group Tn is a right-angled Coxeter group generated by n-1 involutions, and the pure twin group PTn is the kernel of the natural surjection from Tn onto the symmetric group on n symbols. In this paper, we investigate some structural aspects of these groups. We derive a formula for the number of conjugacy classes of involutions in Tn, which, quite interestingly, is related to the well-known

Journal Name: Forum Mathematicum Volume: 32 Issue: 5 Pages: i-iv

We study the generalised Iwasawa invariants of ℤpd-extensions of a fixed number field K. Based on an inequality between ranks of finitely generated torsion ℤp⁢[[T1,…,Td]]-modules and their corresponding elementary modules, we prove that these invariants are locally maximal with respect to a suitable topology on the set of ℤpd-extensions of K, i.e., that the generalised Iwasawa invariants of a ℤpd-extension

Recently, the problem of bounding the sup norms of L2-normalized cuspidal automorphic newforms ϕ on GL2 in the level aspect has received much attention. However at the moment strong upper bounds are only available if the central character χ of ϕ is not too highly ramified. In this paper, we establish a uniform upper bound in the level aspect for general χ. If the level N is a square, our result reduces

We extend the theorems of [M. Greenblatt, Lp Sobolev regularity of averaging operators over hypersurfaces and the Newton polyhedron, J. Funct. Anal. 276 2019, 5, 1510–1527] on Lp to Lsp Sobolev improvement for translation invariant Radon and fractional singular Radon transforms over hypersurfaces, proving Lp to Lsq boundedness results for such operators. Here q≥p but s can be positive, negative, or

We prove the local Lipschitz continuity and the higher differentiability of local minimizers of functionals of the form

In 1977, Colville, Davis, and Keimel [Positive derivations on f-rings, J. Aust. Math. Soc. Ser. A 23 1977, 3, 371–375] proved that a positive derivation on an Archimedean f-algebra A has its range in the set of nilpotent elements of A. The main objective of this paper is to obtain a generalization of the above Colville, Davis and Keimel result to general derivations. Moreover, we give a new version

We establish a sharp higher integrability near the initial boundary for a weak solution to the following p-Laplacian type system:

This paper concerns the study of the Schwartz differential equation {h,τ}=s⁢E4⁡(τ), where E4 is the weight 4 Eisenstein series and s is a complex parameter. In particular, we determine all the values of s for which the solutions h are modular functions for a finite index subgroup of SL2⁡(ℤ). We do so using the theory of equivariant functions on the complex upper-half plane as well as an analysis of

The Cauchy problem of the 2D Zakharov–Kuznetsov equation ∂t⁡u+∂x⁡(∂x⁢x+∂y⁢y)⁡u+u⁢ux=0 is considered. It is shown that the 2D Z-K equation is locally well-posed in the endpoint Sobolev space H-1/4, and it is globally well-posed in H-1/4 with small initial data. In this paper, we mainly establish some new dyadic bilinear estimates to obtain the results, where the main novelty is to parametrize the singularity

We introduce a systematic method to produce left-invariant, non-Ricci-flat Einstein metrics of indefinite signature on nice nilpotent Lie groups. On a nice nilpotent Lie group, we give a simple algebraic characterization of non-Ricci-flat left-invariant Einstein metrics in both the class of metrics for which the nice basis is orthogonal and a more general class associated to order two permutations

We make the polynomial dependence on the fixed representation π in our previous subconvex bound of L⁢(12,π⊗χ) for GL2×GL1 explicit, especially in terms of the usual conductor 𝐂⁢(πfin). There is no clue that the original choice, due to Michel and Venkatesh, of the test function at the infinite places should be the optimal one. Hence we also investigate a possible variant of such local choices in some

In this paper, we study the Lq-Lr boundedness of bi-parameter Fourier integral operators defined by general rough Hörmander class amplitudes.

In this paper, we establish an improved variable coefficient version of the square function inequality, by which the local smoothing estimate Lαp→Lp for the Fourier integral operators satisfying cinematic curvature condition is further improved. In particular, we establish almost sharp results for 2

We show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a characterization of acyclic maps of topological spaces in terms of induced maps of their chain algebras of based loop spaces. In the case of a universal acyclic map we obtain, for a wide class of spaces, an explicit algebraic description

By making use of the generating function method, we derive several summation formulae involving Stirling numbers and Lah numbers as well as other classical combinatorial numbers named after Bernoulli, Euler, Bell, Genocchi, Cauchy, Derangement, Harmonic, Fibonacci and Lucas.

For any real number p∈[1,+∞), we characterise the operations ℝI→ℝ that preserve p-integrability, i.e., the operations under which, for every measure μ, the set ℒp⁢(μ) is closed. We investigate the infinitary variety of algebras whose operations are exactly such functions. It turns out that this variety coincides with the category of Dedekind σ-complete truncated Riesz spaces, where truncation is meant

This paper studies the two-weight estimates of variation and oscillation operators for commutators of singular integrals with weighted BMO functions. A new characterization of weighted BMO spaces via the boundedness of variation and oscillation operators for the iterated commutators of Calderón–Zygmund singular integrals in the two-weight setting is given.

In the present paper, we introduce a new concept of convexity which is generated by a family of endomorphisms of an Abelian group. In Abelian groups, equipped with a translation invariant metric, we define the boundedness, the norm, the modulus of injectivity and the spectral radius of endomorphisms. Beyond the investigation of their properties, our first main goal is an extension of the celebrated

We introduce classes of pairs of weights closely related to Schrödinger operators, which allow us to get two-weight boundedness results for the Schrödinger fractional integral and its commutators. The techniques applied in the proofs strongly rely on one hand, boundedness results in the setting of finite measure spaces of homogeneous type and, on the other hand, Fefferman–Stein-type inequalities that

A skew generalized power series ring R⁢[[S,ω,≤]] consists of all functions from a strictly ordered monoid (S,≤) to a ring R whose support is artinian and narrow, with pointwise addition, and with multiplication given by convolution twisted by an action ω of the monoid S on the ring R. Special cases of this ring construction are skew polynomial rings, skew Laurent polynomial rings, skew power series

In this article, we revisit Rankin–Selberg integrals established by Jacquet, Piatetski-Shapiro and Shalika. We prove the equality of Rankin–Selberg local factors defined with Schwartz–Bruhat functions and the factors attached to good sections, introduced by Piatetski-Shapiro and Rallis. Moreover, we propose a notion of exceptional poles in the framework of good sections. For cases of Rankin–Selberg

Let X be a nonsingular complex projective surface. The Weyl and Zariski chambers give two interesting decompositions of the big cone of X. Following the ideas of [T. Bauer and M. Funke, Weyl and Zariski chambers on K3 surfaces, Forum Math. 24 2012, 3, 609–625] and [S. A. Rams and T. Szemberg, When are Zariski chambers numerically determined?, Forum Math. 28 2016, 6, 1159–1166], we study these two decompositions

Journal Name: Forum Mathematicum Volume: 32 Issue: 4 Pages: i-iv

The aim of this note is to correct the proof of Proposition 2.15 in the original article [M. Doucha, Metrical universality for groups, Forum Math. 29 2017, 4, 847–872].

We prove a uniqueness type theorem for (weak, total) integrals on a Frobenius cowreath in a monoidal category. When the cowreath is, moreover, pre-Galois, we construct a Morita context relating the subalgebra of coinvariants and a certain wreath algebra. Then we see that the strictness of the Morita context is related to the Galois property of the cowreath and the existence of a weak total integral

In this paper we discuss coefficient problems for functions in the class 𝒞0⁢(k). This family is a subset of 𝒞, the class of close-to-convex functions, consisting of functions which are convex in the positive direction of the real axis. Our main aim is to find some bounds of the difference of successive coefficients depending on the fixed second coefficient. Under this assumption we also estimate

Solutions of Rough Differential Equations (RDE) may be defined as paths whose increments are close to an approximation of the associated flow. They are constructed through a discrete scheme using a non-linear sewing lemma. In this article, we show that such solutions also solve a fixed point problem by exhibiting a suitable functional. Convergence then follows from consistency and stability, two notions

Classical Castelnuovo Lemma shows that the number of linearly independent quadratic equations of a nondegenerate irreducible projective variety of codimension c is at most (c+12) and the equality is attained if and only if the variety is of minimal degree. Also G. Fano’s generalization of Castelnuovo Lemma implies that the next case occurs if and only if the variety is a del Pezzo variety. Recently

A generalised Postnikov tower for a space X is a tower of principal fibrations with fibres generalised Eilenberg–MacLane spaces, whose inverse limit is weakly homotopy equivalent to X. In this paper we give a characterisation of a polyhedral product ZK⁢(X,A) whose universal cover either admits a generalised Postnikov tower of finite length, or is a homotopy retract of a space admitting such a tower

We deal with instanton bundles on the product ℙ1×ℙ2 and the blow up of ℙ3 along a line. We give an explicit construction leading to instanton bundles. Moreover, we also show that they correspond to smooth points of a unique irreducible component of their moduli space.