Related papers: On the residue method for period integrals
New time-series analysis tools are needed in disciplines as diverse as astronomy, economics and meteorology. In particular, the increasing rate of data collection at multiple wavelengths requires new approaches able to handle these data.…
We give examples of endperiodic automorphisms.
A space of modular iterated integrals sits inside the space of real analytic modular forms. We present a theorem for producing length three modular iterated integrals which are not simply combinations of real analytic Eisenstein series;…
This paper exposes the underlying mechanism for obtaining second integral moments of $GL_2$ automorphic $L$--functions over an arbitrary number field. Here, moments for $GL_2$ are presented in a form enabling application of the structure of…
We present a prescription to calculate the quadratic and logarithmic divergent parts of several integrals employing a cutoff in a coherent way, i.e. in total agreement with symmetry requirements. As examples we consider one-loop Ward…
In autonomous differential equations where a single first integral is present, periodic orbits are well-known to belong to one-parameter families, parameterized by the first integral's values. This paper shows that this characteristic…
In the case of split $GSpin$ groups, we prove an equality of $L$-functions between automorphic local $L$-functions defined by the Langlands-Shahidi method and local Artin $L$-functions. Our method of proof is based on previous results of…
We introduce new methods in pseudo-isotopy and embedding space theory. As an application we introduce an invariant that detects nontrivial loops of embedded 2-spheres in $S^{2} \times S^{2}$ and in connected sums of $S^{2} \times S^{2}$.…
We prove a cohomological formula for non-critical residues of degree eight automorphic $L$-functions of $\mathrm{GSp}(4) \times \mathrm{GL}(2)$ in the spirit of Beilinson conjecture. We rely on the cohomological interpretation of an…
We use Stein characterizations to obtain new moment-type estimators for the parameters of three classical spherical distributions (namely the Fisher-Bingham, the von Mises-Fisher, and the Watson distributions) in the i.i.d. case. This leads…
This note presents a method to study center families of periodic orbits of complex holomorphic differential equations near singularities, based on some iteration properties of fixed point indices. As an application of this method, we will…
Multivariate residues appear in many different contexts in theoretical physics and algebraic geometry. In theoretical physics, they for example give the proper definition of generalized-unitarity cuts, and they play a central role in the…
Schlesinger transformations are discrete monodromy preserving symmetry transformations of the classical Schlesinger system. Generalizing well-known results from the Riemann sphere we construct these transformations for isomonodromic…
Einstein's field equations for timelike self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are…
We present a method derived from Laplace transform theory that enables the evaluation of fractional integrals. This method is adapted and extended in a variety of ways to demonstrate its utility in deriving alternative representations for…
We study the rotational structures of aperiodic tilings in Euclidean space of arbitrary dimension using topological methods. Classical topological approaches to the study of aperiodic patterns have largely concentrated just on translational…
This report discusses two new ideas for using perturbation methods to solve the time-independent Schr\"odinger equation. The first concept begins with rewriting the perturbation equations in a form that is closely related to matrix…
In this paper, we will consider a kind of infinite dimensional Hamiltonian system(HS), by the method of saddle point reduction, topology degree and the index, we will get the existence of periodic solution for (HS).
For a large class of systems of o.d.e.'s which have first integrals, the method of arrays yields the following results: i) The first integrals $I$ can be found by solving systems of linear equations. ii) How the first integral $I$ responds…
This work is the second in a series, following Part I (Algebra Number Theory 18.10 (2024)) and preceding Part III (Math. Ann. 391.1 (2025)). We continue our investigation of spectral moments of $\hbox{GL}(3)\times \hbox{GL}(2)$…