Related papers: Explicit Gross-Zagier and Waldspurger Formulae
We prove an averaging formula for the canonical archimedean height pairing of special divisors with weights over orthogonal and unitary Shimura curves in terms of derivatives of Whittaker functions.
The main goal of this expository article is to survey recent progress on the arithmetic Siegel-Weil formula and its applications. We begin with the classical sum of two squares problem and put it in the context of the Siegel-Weil formula.…
We present an explicit formula for the deformation quantization on K\"{a}hler manifolds.
Jacobi-Trudy formula for a generalisation of Schur polynomials related to any sequence of orthogonal polynomials in one variable is given. As a corollary we have Giambelli formula for generalised Schur polynomials.
We establish an explicit formula for the general solution of the Benjamin-Ono equation on the torus and on the line. Contents 1. Introduction 1 1.1. The Benjamin-Ono equation 1 1.2. The Lax pair 2 1.3. The explicit formula on the torus 3…
We give new integral and series representations of the Hurwitz zeta function. We also provide a closed-form expression of the coefficients of the Laurent expansion of the Hurwitz-zeta function about any point in the complex plane.
We provide explicit formulas for quadratic Gauss sums over $\mathbb{Z}^n/c\mathbb{Z}^n$, which generalize some of the existing formulas, e.g., Skoruppa and Zagier's (for $n=2$), and Iwaniec and Kowalski's (for arbitrary $n$). We then give…
In this paper, we work out some explicit formulae for double nonlinear Euler sums involving harmonic numbers and alternating harmonic numbers. As applications of these formulae, we give new closed form representations of several quadratic…
Some forms of qKdV type equations are indicated which arise from Virasoro considerations.
We introduce, for every $\mathbb{Z}$-graded manifold, a formal exponential map defined in a purely algebraic way and study its properties. As an application, we give a simple new construction of a Fedosov type resolution of the algebra of…
We establish a sharp bilinear estimate for the Klein--Gordon propagator in the spirit of recent work of Beltran--Vega. Our approach is inspired by work in the setting of the wave equation due to Bez, Jeavons and Ozawa. As a consequence of…
We prove an explicit formula of the Berezin star product on Kaehler manifolds. The formula is expressed as a summation over certain strongly connected digraphs. The proof relies on a combinatorial interpretation of Englis' work on the…
We construct an Euler system associated to regular algebraic, essentially conjugate self-dual cuspidal automorphic representations of GL(3) over imaginary quadratic fields, using the cohomology of Shimura varieties for GU(2, 1).
We prove an equivariant Grothendieck-Ogg-Shafarevich formula. This formula may be viewed as an \'etale analogue of well-known formulas for Zariski sheaves generalizing the classical Chevalley-Weil formula. We give a new approach to those…
Euler Maclaurin formulas for a polytope express the sum of the values of a function over the lattice points in the polytope in terms of integrals of the function and its derivatives over faces of the polytope or its expansions. Exact Euler…
We consider some variations on the classical method of Runge for effectively determining integral points on certain curves. We first prove a version of Runge's theorem valid for higher-dimensional varieties, generalizing a uniform version…
We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial…
We give a survey of the Lagrange inversion formula, including different versions and proofs, with applications to combinatorial and formal power series identities.
The general SU(N) form factor formula is constructed. Exact form factors for the field, the energy momentum and the current operators are derived and compared with the 1/N-expansion of the chiral Gross-Neveu model and full agreement is…
We present some old and new results on dispersive estimates for Schroedinger equations.