Related papers: Partial sums of Horadam sequences: sum-free repres…
A procedure is described that makes use of the generating function of characters to obtain a new generating function $H$ giving the multiplicities of each weight in all the representations of a simple Lie algebra. The way to extract from…
The Fibonacci number is the residue of a rational function, from which follows that Fibonacci number summation identities can be derived with the integral representation method, a method also used to derive combinatorial identities. A…
The present note considers a certain family of sums indexed by the set of fixed length compositions of a given number. The sums in question cannot be realized as weighted compositions. However they can be be related to the hypergeometric…
We give two general transformations that allows certain quite general basic hypergeometric multi-sums of arbitrary depth (sums that involve an arbitrary sequence $\{g(k)\}$), to be reduced to an infinite $q$-product times a single basic…
Sum rules are derived relating mean squared charge radii of the pseudoscalar mesons with the convergent integral of the difference of hadron photoproduction cross-sections on pseudoscalar mesons.
We give some theoretical and computational results on "random" harmonic sums with prime numbers, and more generally, for integers with a fixed number of prime factors.
We investigate fractional sums of arithmetic functions over products of two or three integers, with emphasis on fixed greatest common divisors and multiplicative weights. Let $f$ be an arithmetic function satisfying $f(n) \ll n^\alpha$ for…
For any root system corresponding to a semisimple simply-laced Lie algebra a logarithmic CFT is constructed. Characters of irreducible representations were calculated in terms of theta functions.
Consider the representation of a rational number in the form, associated with "centered" Euclidean algorithm. We prove a new formula for the limit distribution function for sequences of rationals with bounded sum of partial quotients.
Combining the derivative operator with a binomial sum from the telescoping method, we establish a family of summation formulas involving generalized harmonic numbers.
We give a survey on the different results involving the topological structure of subsums of null sequences.
In this article, we explore a series of elementary yet insightful results involving integrals related to Gaussian sums. Using techniques rooted in classical calculus, we derive several identities and evaluate nontrivial definite integrals…
Partial zeta functions of algebraic varieties over finite fields generalize the classical zeta function by allowing each variable to be defined over a possibly different extension field of a fixed finite field. Due to this extra variation…
This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…
We consider a variant on the Tetranacci sequence, where one adds the previous four terms, then divides the sum by two until the result is odd. We give an algorithm for constructing "initially division-poor" sequences, where over an initial…
Power series in which the summand satisfies a linear recurrence relation with polynomial coefficients are shown to be the solution of a linear differential or algebraic equation. Solving the associated differential or algebraic equation…
This paper introduces a symbolic calculus-based approach for deriving closed-form expressions for the sums of arithmetic sequences. The method extends beyond constant-difference sequences to those with polynomially increasing steps,…
We solve an elementary number theory problem on sums of fractional parts, using methods from group theory. We apply our result to deduce the finiteness of certain monodromy representations.
We study sums with multiplicative functions that take values over a non-homogenous Beatty sequence. We then apply our result in a few special cases to obtain asymptotic formulas such as the number of integers in a Beatty sequence…
We present a variety of prime-generating constructions that are based on sums of primes. The constructions come in all shapes and sizes, varying in the number of dimensions and number of generated primes. Our best result is a construction…