Effective counting for discrete lattice orbits in the plane via Eisenstein series

Effective Lower Bounds for L(1, Χ) via Eisenstein Series

a time-series analysis of the demand for life insurance in iran

با توجه به تجزیه و تحلیل داده ها ما دریافتیم که سطح درامد و تعداد نمایندگیها باتقاضای بیمه عمر رابطه مستقیم دارند و نرخ بهره و بار تکفل با تقاضای بیمه عمر رابطه عکس دارند

Eisenstein Series*

group GC defined over Q whose connected component G 0 Q has no rational character. It is also necessary to suppose that the centralizer of a maximal Q split torus of G0C meets every component of GC. The reduction theory of Borel applies, with trivial modifications, to G; it will be convenient to assume that Γ has a fundamental set with only one cusp. Fix a minimal parabolic subgroup P 0 C defin...

The simplest Eisenstein series

We explain some essential aspects of the simplest Eisenstein series for SL2(Z) on the upper half-plane H. There are many different proofs of meromorphic continuation and functional equation of the simplest Eisenstein series for Γ = SL2(Z). We will follow [Godement 1966a] rewriting of a Poisson summation argument that appeared in [Rankin 1939], if not earlier. This argument is the most elementar...

Counting Singular Plane Curves via Hilbert Schemes

Consider the following question. Given a suitable linear series L on a smooth surface S, how many curves in L have a given analytic or topological type of singularity? By “suitable” linear series with respect to a type of singularity, we mean that there are finitely many curves with the singularity in the linear series and their codimension is maximal. Our approach to this question is to expres...