Related papers: Explicit Gross-Zagier and Waldspurger Formulae

We prove the equivalence between two explicit expressions for two-point Witten-Kontsevich correlators obtained by M. Bertola, B. Dubrovin, D. Yang and by P. Zograf.

A new explicit formula is proved for the contribution of the major arcs in the Goldbach and Generalized Twin Prime Problem, in which the level of the major arcs can be chosen very high. This will have many applications in the approximations…

In this short note, we present certain generalized versions of the commutator formulas of some natural operators on manifolds, and give some applications.

We obtain an explicit combinatorial formula for certain parabolic Kostka-Shoji polynomials associated with the cyclic quiver, generalizing results of Shoji and of Liu and Shoji.

Recently the new q-Euler numbers are defined. In this paper we derive the the Kummer type congruence related to q-Euler numbers and we introduce some interesting formulae related to these q-Euler numbers.

We prove a general form of Green Formula and Cauchy Integral Theorem for arbitrary closed rectifiable curves in the plane.

The result of Siegel that the Tamagawa number of $SL_r$ over a function field is 1 has an expression purely in terms of vector bundles on a curve, which is known as the Siegel formula. We prove an analogous formula for vector bundles with…

In this article, we enumerate all Shimura curves X^D_0(N) of genus at most two.

We classify curves in the moduli space of curves that are both Shimura- and Teichmueller curves: Except for the moduli space of genus one curves there is only a single such curve. We start with a Hodge-theoretic description of Shimura…

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 provide direct elementary proofs of several explicit expressions for Bernoulli numbers and Bernoulli polynomials. As a byproduct of our method of proof, we provide natural definitions for generalized Bernoulli numbers and polynomials of…

We present a construction of the explicit Hodge decomposition for $\bar\partial$-equation on Riemann surfaces.

This paper gives new explicit formulas for sums of powers of integers and their reciprocals.

A method is given to construct globally analytic (in space and time) exact solutions to the focusing cubic nonlinear Schrodinger equation on the line. An explicit formula and its equivalents are presented to express such exact solutions in…

Extensions and generalizations of Alzer's inequality; which is of Wirtinger type are proved. As applications, sharp trapezoid type inequality and sharp bound for the geometric mean are deduced.

We give a method to construct explicitly a supersingular curve of given genus g in characteristic 2.

In the paper we present some new inversion formulas and two new formulas for Stirling numbers.

We give explicit expressions for higher order convolutions of Cauchy numbers, either as one single integral or in terms of the Stirling numbers of the first and second kinds.

In this article, we classify the characters associated to algebraic points on Shimura curves of $\Gamma_0(p)$-type, and over a quadratic field we show that there are at most elliptic points on such a Shimura curve for every sufficiently…

We prove two explicit formulae for one-part double Hurwitz numbers with completed 3-cycles. We define "combinatorial Hodge integrals" from these numbers in the spirit of the celebrated ELSV formula. The obtained results imply some explicit…