TY - JOUR
T1 - Solutions of equations involving the modular j function
AU - ETEROVIC, SEBASTIAN
AU - HERRERO MIRANDA, SEBASTIAN DANIEL
N1 - Funding Information:
The first author was partially funded by CONICYT PFCHA/Doctorado Becas Chile/2015-72160240 and the NSF RTG grant DMS-1646385. The second author was partially funded by CONICYT FONDECYT/Postdoctorado Nacional 3190086.
Publisher Copyright:
© 2021 American Mathematical Society. All rights reserved.
PY - 2021
Y1 - 2021
N2 - Inspired by work done for systems of polynomial exponential equations, we study systems of equations involving the modular j function. We show general cases in which these systems have solutions, and then we look at certain situations in which the modular Schanuel conjecture implies that these systems have generic solutions. An unconditional result in this direction is proven for certain polynomial equations on j with algebraic coefficients.
AB - Inspired by work done for systems of polynomial exponential equations, we study systems of equations involving the modular j function. We show general cases in which these systems have solutions, and then we look at certain situations in which the modular Schanuel conjecture implies that these systems have generic solutions. An unconditional result in this direction is proven for certain polynomial equations on j with algebraic coefficients.
UR - http://www.scopus.com/inward/record.url?scp=85105319352&partnerID=8YFLogxK
U2 - 10.1090/tran/8244
DO - 10.1090/tran/8244
M3 - Article
AN - SCOPUS:85105319352
VL - 374
SP - 3971
EP - 3998
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 6
ER -