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On sums involving products of three binomial coefficients
Central binomial coefficients super congruences Catalan numbers
2011/1/21
In this paper we study congruences for sums of terms related to cubes of central binomial coefficients.
We present a hybrid approach to bounding exponential sums over kth powers via Vinogradov's mean value theorem, and derive estimates of utility for exponents k of intermediate size.
On sums of Ramanujan sums
sums of Ramanujan sums
2010/12/10
In this note, we study the moments of the average of the Ramanujan sum. To be precise,we want to evaluate the sums Ck(x, y) =Xn≤y\ Xq≤x cq(n)k.
Faulhaber's Theorem on Power Sums
Faulhaber's theorem power sum alternating sum r-fold power sum r-fold alternating power sum Bernoulli polynomial Euler polynomial
2014/6/3
We observe that the classical Faulhaber's theorem on sums of odd powers also holds for an arbitrary arithmetic progression, namely, the odd power sums of any arithmetic progression a+b, a+2b, ..., a+n...
Conditioned limit theorems for weighted sums of random sequence
Jamison type weighted sums stability conditionally dominated random sequence
2010/9/10
Some notions of conditionally dominated random variables are introduced and characterized, Under rather minimal assumptions on random variables {X,Xn, n ≥ 1}, some limit theorems of Jamison’s type of ...
The distributions of sums, products and ratios of inverted bivariate beta distribution
Bivariate inverted beta distributions Sums Ratios Percentiles
2010/9/14
In this paper we derive the exact distributions of sums, products, and ratios of two random variables when they follow the bivariate inverted beta distribution. Forms of the probability density functi...
A Bound on the Deviation Probability for Sums of Non-Negative Random Variables
Deviation bounds Bernstein's inequality Hoeffdings inequality
2008/7/3
A simple bound is presented for the probability that the sum of nonnegative independent random variables is exceeded by its expectation by more than a positive number t. If the variables have the same...
A Note On Sums Of Powers Which Have A Fixed Number Of Prime Factors
Sums of powers Numbers with $k$ prime factors
2008/7/3
A Note On Sums Of Powers Which Have A Fixed Number Of Prime Factors.
Corrigendum to "On Short Sums of Certain Multiplicative Functions"
Corrigendum Short sums Integer points
2008/7/2
Corrigendum to "On Short Sums of Certain Multiplicative Functions".
Inequalities for Chains of Normalized Symmetric Sums
Symmetric inequalities Cyclic inequalities Inequalities for sums
2008/7/1
Inequalities for Chains of Normalized Symmetric Sums.
L'Hospital Type Rules for Monotonicity: Applications to Probability Inequalities for Sums of Bounded Random Variables
L'Hospital's Rule Monotonicity Probability inequalities Sums of independent random variables Student's statistic
2008/7/1
This paper continues a series of results begun by a l'Hospital type rule for monotonicity, which is used here to obtain refinements of the Eaton-Pinelis inequalities for sums of bounded independent ra...
Matrix Equalities and Inequalities Involving Khatri-Rao and Tracy-Singh Sums
Kronecker product (sum) Hadamard product (sum) Khatri-Rao product (sum) Tracy-Singh product (sum) Positive (semi)definite matrix Unitarily invariant norm Spectral norm P-norm Moore-Penrose inverse
2008/6/30
The Khatri-Rao and Tracy-Singh products for partitioned matrices are viewed as generalized Hadamard and generalized Kronecker products, respectively. We define the Khatri-Rao and Tracy-Singh sums for ...
Neighbourhoods and Partial Sums of Starlike Functions Based on Ruscheweyh Derivatives
Univalent Starlike Convex
2008/6/30
Neighbourhoods and Partial Sums of Starlike Functions Based on Ruscheweyh Derivatives.
Partial Sums Of Certain Meromorphic $p-$Valent Functions
Partial sums Meromorphic $p$-valent starlike functions Meromorphic $p$-valent convex functions
2008/6/27
In this paper we establish some results concerning the partial sums of meromorphic p-valent starlike functions and meromorphic p-valent convex functions.
On Short Sums of Certain Multiplicative Functions
Multiplicative Functions Short Sums Integer points close to a curve
2008/6/27
We use the recent theory of integer points close to a smooth curve developed by Huxley-Sargos and Filaseta-Trifonov to get an asymptotic formula for short sums of a class of multiplicative functions. ...