Related papers: Explicit Gross-Zagier and Waldspurger Formulae
We interpret the "explicit formulas" in the sense of analytic number theory for the zeta function of an elliptic curve over a finite field as a transversal index theorem on a 3-dimensional laminated space.
For a smooth projective curve, we derive a closed formula for the generating series of its Gromov--Witten invariants in genus $g$ and degree zero. It is known that the calculation of these invariants can be reduced to that of the…
We Study versions of Cauchy formula in more general algebras than the complex case.
Relative orbifold Gromov-Witten theory is set-up and the degeneration formula is given.
A formula for Schur $Q$-functions is presented which describes the action of the Virasoro operators. For a strict partition, we prove a concise formula for $L_{-k}Q_{\lambda}$, where $L_{-k}$ $(k\geq 1)$ is the Virasoro operator.
The purpose of this article is to give an explicit formula for all curves of constant torsion $\tau$ in the unit two-sphere $S^2(1)$. These curves and their basic properties have been known since the 1890's, and some of these properties are…
We produce several algebraic curves, some well--known, some new, out of circles, by means of two classical (mutually reciprocal) algebraic methods: blow--down and blow--up.
Generating Hilbert curves in Z^2 using L-systems appears to be efficient and easy
We prove an analogue of Gutzmer's formula for Hermite expansions. As a consequence we obtain a new proof of a characterisation of the image of $ L^2(\R^n) $ under the Hermite semigroup. We also obtain some new orthogonality relations for…
For quadratic curves over $F_p$, the number of solutions, which is governed by an analogue of the Mordell-Weil group, is expressed with the Legendre symbol of a coefficient of quadratic curves. Focusing on the number of solutions, a…
In the paper, the authors review some explicit formulas and establish a new explicit formula for Bernoulli and Genocchi numbers in terms of Stirling numbers of the second kind.
The paragrassmann calculus proposed earlier is applied to constructing paraconformal transformations and paragrassmann generalizations of the Virasoro-Neveu-Schwarz-Ramond algebras.
A holomorphic representation formula for special parabolic hyperspheres is given.
Let F be a non-archimedian local field of characteristic 0, and O the ring of integres in F. We give an explicit formula for the Siegel series of a half-integral matrix over O. This formula expresses the Siegel series of a half-integral…
We prove a refinement of the results of Gross and Zagier on prime factorizations of singular moduli.
We give a cycle-theoretic proof of the Gross-Zagier conjecture in weight four for several modular curves of genus zero.
We obtain an equivariant class formula for z-deformation of t-modules. Under mild conditions, it allows us to get an equivariant class formula for t-modules.
We describe an algorithm for computing the Picard-Fuchs equation for a family of twists of a fixed elliptic surface. We then apply this algorithm to obtain the equation for several examples, which are coming from families of Kummer surfaces…
Exact and explicit expressions for the variogram of first--order intrinsic autoregressions have not been known. Various asymptotic expansions and approximations have been used to compute the variogram. In this note, an exact and explicit…
We compute the arithmetic volumes of integral models of unitary Shimura curves. This establishes the base case of an inductive argument to compute the arithmetic volumes of unitary Shimura varieties of higher dimension, to appear in…