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We prove congruences between cuspidal newforms and Eisenstein series of prime level,
which generalize Ramanujan's congruence. Such congruences were recently found by …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

Mein Promotionsthema liegt in der Schnittmenge von Arithmetik und Funktionentheorie. Es
betrifft eine neue Methode, um elliptische Modulformen zu studieren. Elliptische …