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Surfaces associated to zeros of automorphic L-functions

Conjecture Pair Correlation Surface

This is joint work with Debmalya Basak and Alexandru Zaharescu. I have had the opportunity to present this paper at the UIUC Number Theory Seminar and at the 2024 Fall Central Sectional Meeting at the University of Texas, San Antonio. I also have helped present an earlier version of this project at Joint PU/IAS Number Theory seminar. My contributions begins at 46:49. To the right, you can see what we call the Pair Correlation Surface associated to zeros of automorphic L-functions or the PCS. Find out more about the surfaces and one other in the paper and the website.

Sign changes of the error term in the Piltz divisor problem

Picture of Cruz Castillo

This is joint work with Siegfred Baluyot. I have had the opportunity to present this paper at UIUC Number Theory Seminar and CRG L-functions Weekly Seminars. I presented at two poster sessions at MAGNTS and  IPENTS summer school at UBC Okanagan. Here are the links to the slides, poster, and arxiv post.