3 papers
math.AG2025
On polynomial automorphisms of Nagata type
Jorge A. C. Huarcaya, Joe Palacios
We define a family of polynomial ring homomorphisms generalizing the well-known Nagata automorphism. We establish necessary and sufficient conditions under which these homomorphism…
math.GR2025
The sectional number of a group homomorphism
Cesar A. Ipanaque Zapata, Joe Palacios
We explore the notion of sectional number of a group homomorphism, leading to a generalization of the covering number of a group, and present several characterizations when the sec…
math.NT2025
Partitions into Sums of Two Squares
Jaime Palacios
We use a variation of the Circle Method, along with the Saddle Point Method, to obtain an asymptotic formula for the number of partitions of a number n into integers which are sums…