Abstract We systematically find conditions which yield locally uniform convergence in the Fourier inversion formula in one and higher dimensions. We apply the gained knowledge to the complex inversion formula of the Laplace transform to extend known results for Banach space-valued functions and, specifically, for $$C_0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>C</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> -semigroups.

Abstract We consider the $$L^{2}$$ L 2 -boundedness of the solution of the Cauchy problem for a wave equation with time-dependent wave speeds. We treat it in the one-dimensional Euclidean space $$\textbf{R}$$ R . We adopt a simple multiplier method by using a special property of the one dimensional space.

Using the decomposition of Jacobians with group action, we prove the non-existence of some Shimura subvarieties in the moduli space of ppav Ag arising from families of dihedral and quaternionic covers of the complex projective line P1.

Recent work by Craig, van Ittersum, and Ono constructs explicit expressions in the partition functions of MacMahon that detect the prime numbers. Furthermore, they define generalizations, the MacMahonesque functions, and prove there are infinitely many such expressions in these functions. Here, we show how to modify and adapt their construction to detect cubes of primes as well as primes in arithmetic progressions.

A base for a permutation group G acting on a set Ω is a sequence B of points of Ω such that the pointwise stabiliser GB is trivial. The base size of G is the size of a smallest base for G. We derive a character theoretic formula for the base size of a class of groups admitting a certain kind of irreducible character. Moreover, we prove a formula for enumerating the non-equivalent bases for G of size l∈N. As a consequence of our results, we present a very short, entirely algebraic proof of the formula of Mecenero and Spiga for the base size of the symmetric group Sn acting on the k-element subsets of {1,2,3,…,n}. Our methods also provide a formula for the base size of many product type permutation groups.