arXiv subjects

Joachim Mahnkopf

Publications and source records attributed to Joachim Mahnkopf.

4 recordsLinked to original sources

arXiv2013

On mod $p^c$ transfer and applications

We study a mod $p^c$ analog of the notion of transfer for automorphic forms. Instead of existence of eigenforms, such transfers yield congruences between eigenforms but, like transfers, we show that they can be established by a comparison of trace formulas. This rests on the properties of mod $p^c$ reduced multiplicities which count congruences between eigenforms. As an application we construct finite slope $p$-adic {\it continuous} families of Siegel eigenforms using a comparison of trace formulas.

math.NT↗

arXiv2013

On Truncation of irreducible representations of Chevalley groups

We prove part of a higher rank analogue of the Mazur-Gouvea Conjecture. More precisely, let $\tilde{\bf G}$ be a connected, reductive ${\Bbb Q}$-split group and let $Γ$ be an arithmetic subgroup of $\tilde{\bf G}$. We show that the dimension of the slope $α$ subspace of the cohomology of $Γ$ with values in an irreducible $\tilde{\bf G}$-module $L$ is bounded independently of $L$. The proof is elementary making only use of general principles of the representation theory of algebraic groups; it is based on consideration of certain truncations of irreducible representations of Chevalley groups.

math.NT↗

arXiv2011

Conjugation of Hilbert modular forms and trace formula

We describe (in a representation theoretic setting) a simple comparison of trace formulas, which implies that the conjugate of a Hilbert modular form $f$ by an automorphism of ${\Bbb C}$ again is a Hilbert modular form of the same level and conjugate weight as $f$. This is a Theorem of Shimura for which we obtain a new proof (cf. Theorem 3.3 and Corollary 3.4

math.NT↗

arXiv2008

Traces on Hecke algebras and families of p-adic modular forms

In this preprint we prove that any finite slope modular form fits into a p-adic family of modular forms which is indexed by the weight. Here, the term p-adic family means that p-adic congruences between weights entail certain p-adic congruences between the corresponding modular forms. We also show that the dimension of the slope subspace of the space of modular forms does not depend on the weight. Both statements are predicted by the Mazur-Gouvea Conjecture, which has been proven by Coleman using methods from rigid analytic geometry. In contrast our proof is based on a comparison of (topological) trace formulas.

math.NT↗