Published in Forum Mathematicum
The twin group T n {T_{n}} is a right-angled Coxeter group generated by n - 1 {n-1} involutions, and the pure twin group PT n {\mathrm{PT}_{n}} is the kernel of the natural surjection from T n {T_{n}} 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 c...
Published in Forum Mathematicum
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 na...
Published in Forum Mathematicum
We make the polynomial dependence on the fixed representation π in our previous subconvex bound of L ( 1 2 , π ⊗ χ ) {L(\frac{1}{2},\pi\otimes\chi)} for GL 2 × GL 1 {\mathrm{GL}_{2}\times\mathrm{GL}_{1}} explicit, especially in terms of the usual conductor 𝐂 ( π fin ) {\mathbf{C}(\pi_{\mathrm{fin}})} . There is no clue that the original choice,...
Published in Forum Mathematicum
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 + 1 2 ) {{{c+1}\choose{2}}} 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 ...
Published in Forum Mathematicum
In this paper we discuss coefficient problems for functions in the class 𝒞 0 ( k ) {{\mathcal{C}}_{0}(k)} . This family is a subset of 𝒞 {{\mathcal{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 ...
Published in Forum Mathematicum
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 ...
Published in Forum Mathematicum
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 ...
Published in Forum Mathematicum
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 Z K ( X , A ) {Z_{K}(X,A)} whose universal cover either admits a generalised Postnikov tower of fi...
Published in Forum Mathematicum
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 fram...
Published in Forum Mathematicum
Throughout this paper we show that under certain conditions the method for describing solvable Leibniz (resp. Lie) algebras with given nilradical by means of non-nilpotent outer derivations of the nilradical is also applicable to the case Leibniz (resp. Lie) superalgebras. Moreover, after having established the general method for Lie and Leibniz su...
