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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Hall algebras and graphs of Hecke operators for elliptic curves

Full text
Author(s):
Alvarenga, Roberto [1]
Total Authors: 1
Affiliation:
[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13566590 Sao Carlos, SP - Brazil
Total Affiliations: 1
Document type: Journal article
Source: Israel Journal of Mathematics; SEP 2020.
Web of Science Citations: 0
Abstract

The graph of a Hecke operator encodes all information about the action of this operator on automorphic forms over a global function field. These graphs were introduced by Lorscheid in {[}16] for PGL(2)and generalized to GL(n)in {[}1]. After reviewing some general properties, we explain the connection to the Hall algebra of the function field. In the case of an elliptic function field, we can use structure results of Burban-Schiffmann {[}7] and Fratila {[}8] to develop an algorithm which explicitly calculates these graphs. We apply this algorithm to determine some structure constants and provide explicitly the rank two case in the last section. (AU)

FAPESP's process: 17/21259-3 - Graphs of Hecke Operators and Rational Points
Grantee:Roberto Carlos Alvarenga da Silva Junior
Support type: Scholarships in Brazil - Post-Doctorate