相关论文: The change of variable formula for the Riemann int…

Using a result of recursive function theory and results of the complex analysis of Takeuti, which is based on a type theory and the work of Kreisel, and which gives a conservative extension of first order Peano arithmetic (PA), assuming all…

Because of its relation to the distribution of prime numbers, the Riemann zeta function {\zeta} (s) is one of the most important functions in mathematics. The zeta function is defined by the following formula for any complex number s with…

We show a quite simple second variation formula for Perelman's $\mathcal{W}$-functional along the modified K\"ahler-Ricci flow over Fano manifolds.

In this paper, a positive answer to the Riemann hypothesis is given by using a new result that predict the exact location of zeros of the alternating zeta function on the critical strip.

In this paper, we discuss the value-distribution of the Riemann zeta-function. The authors give some results for the discrepancy estimate and large deviations in the limit theorem by Bohr and Jessen.

The variable change w=exp(u) is applied to establish novel integral representations of the incomplete gamma-function, hypergeometric F-function,confluent hypergeometric /Phi-function and beta-function, and to analyze these functionsas as…

We rewrite Riemann Zeta function as a sum over the primes. Each term of the sum is a product that depends only on the summation index (a prime) and the primes following it.

We show that Riemann surfaces, and separated variables immediately provide classical Poisson commuting Hamiltonians. We show that Baxter's equations for separated variables immediately provide quantum commuting Hamiltonians. The…

We show that the Euler-MacLaurin formula for Riemann sums has an n-dimensional analogue in which intervals on the line get replaced by convex polytopes.

Explicit general constructions of paragrassmann calculus with one and many variables are given. Relations of the paragrassmann calculus to quantum groups are outlined and possible physics applications are briefly discussed. This paper is…

We present a new approach to the study of multiplier ideals in a local, two-dimensional setting. Our method allows us to deal with ideals, graded systems of ideals and plurisubharmonic functions in a unified way. Among the applications are…

We obtain an asymptotic formula for the second discrete moment of the Riemann zeta function over the arithmetic progression $\frac{1}{2} + in$. It shows that the first main term is equal to that of the continuous mean value.

We give an explicit formula for the Bellman function associated with the dual bound related to the unconditional constant of the Haar system.

We discuss the application of the determinantal method to the proof of the Riemann hypothesis. We start from the fact that, if a certain doubly infinite set of determinants are all positive, then the hypothesis is true. This approach…

We introduce a modified Regge calculus for general relativity on a triangulated four dimensional Riemannian manifold where the fundamental variables are areas and a certain class of angles. These variables satisfy constraints which are…

We generalize some classical results for the Schlesinger system of partial differential equations and give the explicit form of its solution, associated with rational matrix functions in general position.

In this paper we present a simple method for deriving an alternative form of the functional equation for Riemann's Zeta function. The connections between some functional equations obtained implicitly by Leonhard Euler in his work "Remarques…

We prove Euler-Lagrange fractional equations and sufficient optimality conditions for problems of the calculus of variations with functionals containing both fractional derivatives and fractional integrals in the sense of Riemann-Liouville.

We give the solution of certain parabolic evolution problems (time-depending perturbations of the heat equation for the harmonic oscillator) as explicit integrals on the Wiener space.

We give an Euler-Maclaurin formula with remainder for the weighted sum of the values of a smooth function on the integral points in a simple integral polytope. Our work generalizes the formula obtained by Karshon, Sternberg and Weitsman in…