Related papers: Explicit Formula for Witten-Kontsevich Tau-Functio…
In this paper we study a group theoretical generalization of the well-known Gauss's formula that uses the generalized Euler's totient function introduced in [11].
We obtain an exact formula for the cubic partition function and prove a conjecture by Banerjee, Paule, Radu and Zeng.
We derive an explicit formula for the Witten-Reshetikhin-Turaev SO(3)-invariants of lens spaces. We use the representation of the mapping class group of the torus corresponding to the Witten-Reshetikhin-Turaev SO(3)-TQFT to give such…
In this letter,we present our conjecture on the connection between the Kontsevich--Witten and the Hurwitz tau-functions. The conjectural formula connects these two tau-functions by means of the $GL(\infty)$ group element. An important…
An integral formula is developed which applies to an essentially arbitrary function. An application is made to the Riemann zeta function.
We give a closed formula for the Conway function of a splice in terms of the Conway function of its splice components. As corollaries, we refine and generalize results of Seifert, Torres, and Sumners-Woods.
A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.
We derive an exact expression for the tachyon $\beta$-function for the Wess-Zumino-Witten model. We check our result up to three loops by calculating the three-loop tachyon $\beta$-function for a general non-linear $\sigma$-model with…
In this paper, we will give a new proof for a known result of the mean square of Riemann zeta-function.
The details for the construction of an explicit formula for the divisors function d(n) = #{d | n} are formalized in this article. This formula facilitates a unified approach to the investigation of the error terms of the divisor problem and…
We derive a new explicit formula in terms of sums over graphs for the $n$-point correlation functions of general formal weighted double Hurwitz numbers coming from the Kadomtsev-Petviashvili tau functions of hypergeometric type (also known…
We discuss some subtleties in connection with the new attempts to provide a firm basis for ths Witten-Veneziano formula.
In this work we derive a functional equation in terms of the Hurwitz-Lerch zeta function along with definite integrals in terms of the incomplete gamma and Hurwitz-Lerch zeta functions. The method used in these derivations is contour…
Leibniz's rule for the $n$-th derivative of a product is a very well known and extremely useful formula. In this article, we introduce an analogous explicit formula for the $n$-th derivative of a quotient of two functions. Later, we use…
We consider solvable matrix models. We generalize Harish-Chandra-Itzykson-Zuber and certain other integrals (Gross-Witten integral and integrals over complex matrices) using the notion of tau function of matrix argument. In this case one…
A quite fast proof of the functional equation of the Riemann zeta function. It is a modification of a proof usually overlooked in Titchmarsh's monograph.
We write down the functional equation of the zeta function of a global field. This equation is implicit in Weil's ``Basic Number Theory''.
We give an explicit formula for the well-known parity result for multiple zeta values as an application of the multitangent functions.
We consider a class of measures absolutely continuous with respect to the distribution of the stopped Wiener process $w(\cdot\wedge\tau)$. Multiple stochastic integrals, that lead to the analogue of the It\^o-Wiener expansions for such…
We give a proof of Alexandrov's conjecture on a formula connecting the Kontsevich-Witten and Hodge tau-functions using only the Virasoro operators. This formula has been confirmed up to an unknown constant factor. In this paper, we show…