Zobrazeno 1 - 10
of 170
pro vyhledávání: '"Raum, Martin"'
Generalizing the well-known construction of Eisenstein series on the modular curves, Siegel-Veech transforms provide a natural construction of square-integrable functions on strata of differentials on Riemannian surfaces. This space carries actions o
Externí odkaz:
http://arxiv.org/abs/2404.06597
Autor:
Keilthy, Adam, Raum, Martin
We relate analytically defined deformations of modular curves and modular forms from the literature to motivic periods via cohomological descriptions of deformation theory. Leveraging cohomological vanishing results, we prove the existence and essent
Externí odkaz:
http://arxiv.org/abs/2404.03519
Autor:
Raum, Martin
While examples of Ramanujan-type congruences are amply available via their relation to Hecke operators, it remains unclear which of them should be considered of combinatorial origin and which of them are mere artifacts of the connection with modular
Externí odkaz:
http://arxiv.org/abs/2404.02672
Autor:
Bruinier, Jan Hendrik, Raum, Martin
The notion of formal Siegel modular forms for an arithmetic subgroup $\Gamma$ of the symplectic group of genus $n$ is a generalization of symmetric formal Fourier-Jacobi series. Assuming an upper bound on the affine covering number of the Siegel modu
Externí odkaz:
http://arxiv.org/abs/2402.06572
Given an odd prime $\ell$ and finite set of odd primes $S_+$, we prove the existence of an imaginary quadratic field whose class number is indivisible by $\ell$ and which splits at every prime in $S_+$. Notably, we do not require that $p \not\equiv -
Externí odkaz:
http://arxiv.org/abs/2305.19272
Autor:
Magnusson, Tobias, Raum, Martin
Given cusp forms $f$ and $g$ of integral weight $k \geq 2$, the depth two holomorphic iterated Eichler-Shimura integral $I_{f,g}$ is defined by ${\int_\tau^{i\infty}f(z)(X-z)^{k-2}I_g(z;Y)\mathrm{d}z}$, where $I_g$ is the Eichler integral of $g$ and
Externí odkaz:
http://arxiv.org/abs/2209.00488
We give a classification of the Harish-Chandra modules generated by the pullback to~$\SL{2}(\RR)$ of \emph{poly}harmonic Maa\ss{} forms for congruence subgroups of~$\SL{2}(\ZZ)$ with exponential growth allowed at the cusps. This extends results of Br
Externí odkaz:
http://arxiv.org/abs/2207.02278
Autor:
Raum, Martin
The Bernstein-Gelfand tensor product functors are endofunctors of the category of Harish-Chandra modules provided by tensor products with finite dimensional modules. We provide an automorphic analogue of these tensor product functors, implemented by
Externí odkaz:
http://arxiv.org/abs/2205.08226
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 forms. We d
Externí odkaz:
http://arxiv.org/abs/2203.15462
We extend a holomorphic projection argument of our earlier work to prove a novel divisibility result for non-holomorphic congruences of Hurwitz class numbers. This result allows us to establish Ramanujan-type congruences for Hurwitz class numbers on
Externí odkaz:
http://arxiv.org/abs/2203.11273