Lacunary eta quotients with identically vanishing coefficients

Authors

Timothy Huber, The University of Texas Rio Grande ValleyFollow
James McLaughlin
Dongxi Ye

Document Type

Article

Publication Date

3-29-2023

Abstract

For |q|<1 , define fi=∏∞n=1(1−qin) , and let (A(q),B(q)) be any of the pairs (f41,f81f22), (f41,f101f23), (f61,f42f21), (f61,f141f42), (f101,f62f21), (f141,f53f1),(f141,f82f21). For any such pair (A(q),B(q)) , define the sequences {a(n)} and {b(n)} to be the coefficients of qn of A(q) and B(q) , respectively. Then for each pair it is shown that a(n) vanishes if and only if b(n) vanishes. In each case, a criterion is given which states precisely when a(n)=b(n)=0 . Moreover, for the pairs (f261,f93f1) , (f261,f162f61) it is shown that a(n)=b(n)=0 if 12n+13 satisfies a criteria of Serre for a(n)=0 .

Comments

© World Scientific Publishing Company.

Electronic version of an article published at https://doi.org/10.1142/S179304212350080X

Recommended Citation

Huber, Timothy, James McLaughlin, and Dongxi Ye. "Lacunary eta quotients with identically vanishing coefficients." International Journal of Number Theory (2023): 1-32. https://doi.org/10.1142/S179304212350080X

Publication Title

International Journal of Number Theory

DOI

https://doi.org/10.1142/S179304212350080X