Generalized Gaussian bounds for discrete convolution powers

Maximal Probabilities of Convolution Powers of Discrete Uniform Distributions

We prove optimal constant over root n upper bounds for the maximal probabilities of nth convolution powers of discrete uniform distributions. For l, n ∈ N := {1, 2, 3, . . .}, let U∗n l denote the nth convolution power of the discrete uniform distribution Ul := 1 l (δ0+ . . .+δl−1). Let u ∗n l denote the density of U ∗n l with respect to counting measure. Thus, writing 1A(x) := 1 if x ∈ A and 1...

Strong exponent bounds for the local Rankin-Selberg convolution

Let $F$ be a non-Archimedean locally compact field‎. ‎Let $sigma$ and $tau$ be finite-dimensional representations of the Weil-Deligne group of $F$‎. ‎We give strong upper and lower bounds for the Artin and Swan exponents of $sigmaotimestau$ in terms of those of $sigma$ and $tau$‎. ‎We give a different lower bound in terms of $sigmaotimeschecksigma$ and $tauotimeschecktau$‎. ‎Using the Langlands...

The convolution inequality for entropy powers

A Discrete Convolution on the Generalized Hosoya Triangle

The generalized Hosoya triangle is an arrangement of numbers where each entry is a product of two generalized Fibonacci numbers. We define a discrete convolution 1 C based on the entries of the generalized Hosoya triangle. We use C and generating functions to prove that the sum of every k-th entry in the n-th row or diagonal of generalized Hosoya triangle, beginning on the left with the first e...

UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES

Let $R$ be a commutative Noetherian ring with non-zero identity and $fa$ an ideal of $R$. Let $M$ be a finite $R$--module of finite projective dimension and $N$ an arbitrary finite $R$--module. We characterize the membership of the generalized local cohomology modules $lc^{i}_{fa}(M,N)$ in certain Serre subcategories of the category of modules from upper bounds. We define and study the properti...