29 citations · 185 across the 37 of their papers we have counts for
9 papers · 1 filter
Automorphic forms for PGL(3) over elliptic function fields. Part 1: Graphs of Hecke operators
Roberto Alvarenga, Oliver Lorscheid, Valdir Pereira Júnior
This is a first part of a series of papers in which we develop explicit computational methods for automorphic forms for GL(3) and PGL(3) over elliptic function fields. In this firs…
Factorizations of tropical and sign polynomials
Alexander Agudelo, Oliver Lorscheid
In this text, we study factorizations of polynomials over the tropical hyperfield and the sign hyperfield, which we call `tropical polynomials' and `sign polynomials', respectively…
Descartes' rule of signs, Newton polygons, and polynomials over hyperfields
Matthew Baker, Oliver Lorscheid
We develop a theory of multiplicities of roots for polynomials over hyperfields and use this to provide a unified and conceptual proof of both Descartes' rule of signs and Newton's…
Automorphic forms for elliptic function fields
Oliver Lorscheid
Let be the function field of an elliptic curve over $\F_q$. In this paper, we calculate explicit formulas for unramified Hecke operators acting on automorphic forms over $F…
Graphs of Hecke operators
Oliver Lorscheid
Let be a curve over $\F_q$ with function field . In this paper, we define a graph for each Hecke operator with fixed ramification. A priori, these graphs can be seen as a co…
Toroidal automorphic forms for function fields
Oliver Lorscheid
The space of toroidal automorphic forms was introduced by Zagier in 1979. Let be a global field. An automorphic form on $\GL(2)$ is toroidal if it has vanishing constant Fourie…