Related papers: Formule de Fateev

We give a simplified proof and an improvement of a recent theorem by A. Grigoriev, placing an upper bound for the number of roots of linear combinations of solutions to systems of linear equations with polynomial or rational coefficients.

We present a far reaching generalization of a factorization theorem by Bhat, Ramesh, and Sumesh (stated first by Asadi) and furnish a very quick proof.

A new class of structured matrices is presented and a closed form formula for their determinant is established. This formula has strong connections with the one for Vandermonde matrices.

In this paper, we prove Raabe-type integral formulas for gamma function via left and right sided Riemann-Liouville fractional integrals. As corollaries, we give the left and right sided repeated integration formulas for the log-gamma and…

The aim of this note is a proof of a recent conjecture of Kellner concerning the number of distinct prime factors of a particular product of primes. The proof uses profound results from analytic number theory, such as Granville-Ramar\'{e}'s…

We present a generalization of a formula of higher order derivatives and give a short proof.

The convex hull of the roots of a classical root lattice is called a root polytope. We determine explicit unimodular triangulations of the boundaries of the root polytopes associated to the root lattices A_n, C_n, and D_n, and compute their…

A series transformation idea inspired by a formula of R. W. Gosper and some asymptotic expansions for the central binomial coefficients leads us to new accurate approximations for the Gamma function.

Two classes of relations for multiple zeta values are handled algebraically. A restricted sum formula is proved by Eie, Liaw and Ong. The derivation relation is proved by Ihara, Kaneko and Zagier. In this paper we show the latter implies…

This note contains a short proof of the functional equation for the zeta function.

We give a simple proof of some explicit formulas of periodic continuants by Chebyshev polynomials of the second kind given by Rozsa.

A new method for continuing the usual Dirichlet series that defines the Riemann zeta function ${\zeta}(s)$ is presented. Numerical experiments demonstrating the computational efficacy of the resulting continuation are discussed.

Spivey presented a new approach to evaluate combinatorial sums by using finite differences. We present some closed forms for sums involving the binomial coefficients, Fibonacci and Lucas numbers in terms of the falling factorial.

Recently N. Levin (Comp. Math. 127 (2001), 1--21) proved the Tate conjecture for ordinary cubic fourfolds over finite fields. In this paper we prove the Tate conjecture for self-products of ordinary cubic fourfolds. Our proof is based on…

This is an elementary note. It corrects a mistake in the reformulation of the Riemann Hypothesis in J. Havil's book Gamma: Exploring Euler's Constant.

We study two families of zeta-like multiple series -- the multiple $\rho$-values and the multiple $\eta$-values -- defined by nested sums with shifted denominators. An explicit factorial formula for $\rho$ reveals its intrinsic…

We intimate deeper connections between the Riemann zeta and gamma functions than often reported and further derive a new formula for expressing the value of $\zeta(2n+1)$ in terms of zeta at other fractional points. This paper also…

This is a largely expository note which applies standard techniques of the theory of Duijstermaat-Heckman measures for compact Lie groups and results of P. Littelmann to prove a generalization of a conjecture of Coquereaux and Zuber.

In this short note we prove a sharp lower bound for the second moment of a lattice Voronoi cell in terms of the respective covering radius. This gives an affirmative answer to a conjecture by Haviv, Lyubashevsky and Regev. We also…

We prove a new linear relation for a q-analogue of multiple zeta values. It is a q-extension of the restricted sum formula obtained by Eie, Liaw and Ong for multiple zeta values.