Related papers: Meromorphic modular forms with rational cycle inte…
We study numerical conformal mappings of planar Jordan domains with boundaries consisting of finitely many circular arcs and compute the moduli of quadrilaterals for these domains. Experimental error estimates are provided and, when…
We formulate a notion of modular form on the double half-plane for half-integral weights and explain its relationship to the usual notion of modular form. The construction we provide is compatible with certain physical considerations due to…
A 2022 result of Karpenko establishes a conjecture of Hoffmann-Totaro on the possible values of the first higher isotropy index of an arbitrary anisotropic quadratic form of given dimension over an arbitrary field. For nondegenerate forms,…
A complete classification and character formulas for finite-dimensional irreducible representations of the rational Cherednik algebra of type A is given. Less complete results for other types are obtained. Links to the geometry of affine…
We review properties of closed meromorphic $1$-forms and of the foliations defined by them. We present and explain classical results from foliation theory, like index theorems, the existence of separatrices, and resolution of singularities…
There is a classical geometric construction which uses a binary quadratic form to define an involution on the space of binary d-ics. We give a complete characterization of a general class of such involutions which are definable using…
We investigate modularity of elliptic curves over a general totally real number field, establishing a finiteness result for the set non-modular $j$-invariants. By analyzing quadratic points on some modular curves, we show that all elliptic…
We form a sequence of oblong matrices by evaluating an integrable vector-valued function along the orbit of an ergodic dynamical system. We obtain an almost sure asymptotic result for the permanents of those matrices. We also give an…
Basic facts and definitions of conformal moduli of rings and quadrilaterals are recalled. Some computational methods are reviewed. For the case of quadrilaterals with polygonal sides, some recent results are given. Some numerical…
We prove a geometric formula for the cycle integrals of Parson's weight 2k modular integrals in terms of the intersection angles of geodesics on modular curves. Our result is an analog for modular integrals of a classical formula for the…
We study two-dimensional classically integrable field theory with independent boundary condition on each end, and obtain three possible generating functions for integrals of motion when this model is an ultralocal one. Classically…
We observe structure in the sequences of quotients and remainders of the Euclidean algorithm with two families of inputs. Analyzing the remainders, we obtain new algorithms for computing modular inverses and representating prime numbers by…
We study some functorial properties of certain sheaves of meromorphic forms on reduced complex space; particulary, the meromorphic forms which extend holomorphicaly on any desingularisation. The purpose concern their behavior under pull…
We develop the version of the $J$-invariant for hermitian forms over quadratic extensions in a similar way Alexander Vishik did it for quadratic forms. This discrete invariant contains informations about rationality of algebraic cycles on…
We investigate the behaviour of elliptic Feynman integrals under modular transformations. This has a practical motivation: Through a suitable modular transformation we can achieve that the nome squared is a small quantity, leading to fast…
In this paper, with the help of trinomial coefficients we study some arithmetic properties of certain determiants involving reciprocals of binary quadratic forms over finite fields.
We formulate a method to find the meromorphic solutions of higher-order recurrence relations in the form of the sum over poles with coefficients defined recursively. Several explicit examples of the application of this technique are given.…
The theory of modular deformations is generalized for the category of complex analytic polyhedra which includes germs of complex space as well as any compact complex analytic space. The objective of the theory is a construction of fine…
In the moduli space of quadratic differentials over complex structures on a surface, we construct a set of full Hausdorff dimension of points with bounded Teichm\"uller geodesic trajectories.The main tool is quantitative nondivergence of…
We use the fermionic construction of two-matrix model partition functions to evaluate integrals over rational symmetric functions. This approach is complementary to the one used in the paper ``Integrals of Rational Symmetric Functions,…