Computing classical modular forms
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[HTML][HTML] A generalization of Ramanujan's congruence to modular forms of prime level
R Gaba, AA Popa - Journal of Number Theory, 2018 - Elsevier
We prove congruences between cuspidal newforms and Eisenstein series of prime level,
which generalize Ramanujan's congruence. Such congruences were recently found by …
which generalize Ramanujan's congruence. Such congruences were recently found by …
On the trace formula for Hecke operators on congruence subgroups
A Popa - Proceedings of the American Mathematical Society, 2018 - ams.org
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 certain …
finite index subgroups of the modular group. The proof uses algebraic properties of certain …
A note on the trace formula
E Assaf - arXiv preprint arXiv:2311.03523, 2023 - arxiv.org
arXiv:2311.03523v1 [math.NT] 6 Nov 2023 Page 1 arXiv:2311.03523v1 [math.NT] 6 Nov 2023 A
NOTE ON THE TRACE FORMULA ERAN ASSAF Abstract. In this mostly expository note, we …
NOTE ON THE TRACE FORMULA ERAN ASSAF Abstract. In this mostly expository note, we …
An elementary proof of the Eichler–Selberg trace formula
AA Popa, D Zagier - Journal für die reine und angewandte …, 2020 - degruyter.com
We give a purely algebraic proof of the trace formula for Hecke operators on modular forms
for the full modular group SL 2(ℤ), using the action of Hecke operators on the space of …
for the full modular group SL 2(ℤ), using the action of Hecke operators on the space of …
A trace formula for Hecke operators on Fuchsian groups
AA Popa - arXiv preprint arXiv:2306.10396, 2023 - arxiv.org
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 $ V $. The proof is based on …
Fuchsian group of finite covolume, with coefficients in a module $ V $. The proof is based on …
On the trace formula for Hecke operators on congruence subgroups, II
AA Popa - Research in the Mathematical Sciences, 2018 - Springer
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 …
on modular forms for congruence subgroups, expressed as a sum over conjugacy classes …
Finite-dimensional period spaces for the spaces of cusp forms
Let k be a positive integer and P k⊂ C [X] the set of polynomials of degree less than or equal
to k. There exists an isomorphism, called the Eichler–Shimura isomorphism, between the …
to k. There exists an isomorphism, called the Eichler–Shimura isomorphism, between the …
A survey of the number theoretic properties of real analytic modular forms
J Drewitt - 2021 - eprints.nottingham.ac.uk
The purpose of this thesis is to study the number theoretic properties of real analytic modular
forms, which were recently introduced by F. Brown. We begin with a brief review of the …
forms, which were recently introduced by F. Brown. We begin with a brief review of the …
[PDF][PDF] Abstrakte Periodenräume, Projektoren und Spuren von Heckeoperatoren
A Gast - 2018 - core.ac.uk
Mein Promotionsthema liegt in der Schnittmenge von Arithmetik und Funktionentheorie. Es
betrifft eine neue Methode, um elliptische Modulformen zu studieren. Elliptische …
betrifft eine neue Methode, um elliptische Modulformen zu studieren. Elliptische …