8 citations · 31 across the 33 of their papers we have counts for
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A decomposition of Weyl group multiple Dirichlet series for symmetrizable Kac-Moody root systems
Alexandru A. Popa, Jack Walsh
We study twisted Weyl group multiple Dirichlet series attached to symmetrizable Kac-Moody root systems, using the Chinta-Gunnells method to construct their -parts. Our main resu…
Residues of quadratic Weyl group multiple Dirichlet series
Adrian Diaconu, Bogdan Ion, Vicenţiu Paşol +1
We give explicit formulas for the residue of the Chinta-Gunnells average attached to a finite irreducible root system, at the polar divisor corresponding to a simple short root. Th…
A trace formula for Hecke operators on Fuchsian groups
Alexandru A. Popa
In this paper we give a trace formula for Hecke operators acting on the cohomology of a Fuchsian group of finite covolume, with coefficients in a module . The proof is based on…
Quadratic Weyl group multiple Dirichlet series of Type
Adrian Diaconu, Vicenţiu Paşol, Alexandru A. Popa
In this paper and its sequel \cite{DPP}, we investigate the precise relationship between the quadratic affine Weyl group multiple Dirichlet series in the sense of \cite{CG1, BD}, a…
A simple proof of the Eichler-Selberg trace formula
Alexandru A. Popa, Don Zagier
We give a short proof of the trace formula for Hecke operators on modular forms for the modular group, using the action of Hecke operators on the space of period polynomials.
On the trace formula for Hecke operators on congruence subgroups, II
Alexandru A. Popa
In a previous paper, we obtained a general trace formula for double coset operators acting on modular forms for congruence subgroups, expressed as a sum over conjugacy classes. Her…
A generalization of Ramanujan's congruence to modular forms of prime level
Radu Gaba, Alexandru A. Popa
We prove congruences between cuspidal newforms and Eisenstein series of prime level, which generalize Ramanujan's congruence. Such congruences were recently found by Billerey and M…
A combinatorial refinement of the Kronecker-Hurwitz class number relation
Alexandru A. Popa, Don Zagier
We give a refinement of the Kronecker-Hurwitz class number relation, based on a tesselation of the Euclidean plane into semi-infinite triangles labeled by that…
On the trace formula for Hecke operators on congruence subgroups
Alexandru A. Popa
We give a new, simple proof of the trace formula for Hecke operators on modular forms for finite index subgroups of the modular group. The proof uses algebraic properties of certai…
Pair correlation of hyperbolic lattice angles
Florin P. Boca, Alexandru A. Popa, Alexandru Zaharescu
Let be a point in the upper half plane, and let be a discrete, finite covolume subgroup of . We conjecture an explicit formula for the pair corr…
An algebraic property of Hecke operators and two indefinite theta series
Vicentiu Pasol, Alexandru A. Popa
We prove an algebraic property of the elements defining Hecke operators on period polynomials associated with modular forms, which implies that the pairing on period polynomials co…
On the Petersson scalar product of arbitrary modular forms
Vicentiu Pasol, Alexandru A. Popa
We consider a natural extension of the Petersson scalar product to the entire space of modular forms of integral weight for a finite index subgroup of the modular group. W…
Pair correlation of angles between reciprocal geodesics on the modular surface
Florin P. Boca, Vicentiu Pasol, Alexandru A. Popa +1
The existence of the limiting pair correlation for angles between reciprocal geodesics on the modular surface is established. An explicit formula is provided, which captures geomet…