Related papers: On Constant Terms of Eisenstein Series

We obtain a blow-up theorem for regular submanifolds in the Heisenberg group, where intrinsic dilations are used. Main consequence of this result is an explicit formula for the density of (p+1)-dimensional spherical Hausdorff measure…

The temperature inversion properties of the internal energy, E, on odd spheres, and its derivatives, together with their expression in elliptic terms, as expounded in previous papers, are extended to the integrals of E, thence making…

We show that the generalised Stieltjes constants may be represented by infinite series involving logarithmic terms. Some relations involving the derivatives of the Hurwitz zeta function are also investigated

We show that all Eichler integrals, and more generally all "generalized second order modular forms" can be expressed as linear combinations of corresponding generalized second order Eisenstein series with coefficients in classical modular…

We compute the Fourier expansion of vector valued Eisenstein series for the Weil representation associated to an even lattice. To this end, we define certain twists by Dirichlet characters of the usual Eisenstein series associated to…

We study congruences for Eisenstein series on $\mathrm{SL}_2(\mathbb{Z})$ modulo $p^2$, where $p \geq 5$ is prime. It is classically known that all Eisenstein series of weight at least $4$ are determined modulo $p^2$ by those of weight at…

The most fundamental notion in frame theory is the frame expansion of a vector. Although it is well known that these expansions are unconditionally convergent series, no characterizations of the unconditional constant were known. This has…

We specialize the Eichler-Selberg trace formula to obtain trace formulas for the prime-to-level Hecke action on cusp forms for certain congruence groups of arbitrary level. As a consequence, we determine the asymptotic in the prime p of the…

We prove the equality of three conjectural formulas for the Brumer--Stark units. The first formula has essentially been proven, so the present paper also verifies the validity of the other two formulas.

We form real-analytic Eisenstein series twisted by Manin's noncommutative modular symbols. After developing their basic properties, these series are shown to have meromorphic continuations to the entire complex plane and satisfy functional…

We deduce the cyclotomic Iwasawa main conjecture for Hilbert modular cuspforms with complex multiplication from the multivariable main conjecture for CM number fields. To this end, we study in detail the behaviour of the $p$-adic…

This paper studies the non-holomorphic Eisenstein series E(z,s) for the modular surface, and shows that integration with respect to certain non-negative measures gives meromorphic functions of s that have all their zeros on the critical…

We obtain new results on the existence and multiplicity of fixed points of Hammerstein equations in very general cones. In order to achieve this, we combine a new formulation of cones in terms of continuous functionals with fixed point…

Applying the theory of modular forms and Lambert series manipulations we establish an Eisenstein series identity. From this formula we confirm a Lambert series identity conjectured by Gosper. Another Lambert series identity of Gosper is…

W. Luo and P. Sarnak have proved the quantum unique ergodicity property for Eisenstein series on $\rm{PSL}(2,\mathbb{Z}) \backslash H$. We extend their result to Eisenstein series on $\rm{PSL}(2,O) \backslash H^n$, where $O$ is the ring of…

Stembridge introduced the notion of stability for Kronecker triples which generalize Murnaghan's classical stability result for Kronecker coefficients. Sam and Snowden proved a conjecture of Stembridge concerning stable Kronecker triple,…

The Stieltjes constants \gamma_k(a) appear as the coefficients in the regular part of the Laurent expansion of the Hurwitz zeta function \zeta(s,a) about s=1. We present series representations of these constants of interest to theoretical…

Scattering constants are special values of Dirichlet series associated to non-holomorphic Eisenstein series. In this paper we give closed formulas for the scattering constants related to a non-congruence subgroup obtained via a Belyi map of…

Using results from the theory of modular forms, we reprove and extend a result of Romik about lacunary recurrence relations for Eisenstein series.

In this paper we develop a new method to study Iwasawa theory and Eisenstein families for unitary groups $\mathrm{U}(r,s)$ of general signature over a totally real field $F$. As a consequence we prove that for a motive corresponding to a…