My primary research interest revolves around the distribution of zeros of automorphic L-functions. My background in number theory is primarily analytic, but I also take interest in the algebraic aspects of automorphic forms. My most recent work was on partition functions. I am currently interested in q-hypergeometric series and moments of L-functions, and, going forward, I hope to explore these further in my work.
In general, I am always looking to learn new mathematics and number-theoritic concepts I have not come across yet. I take particular pleasure in learning about new advancements in number theory and witnessing the overlap of these sub-branches.
Please email me for a link to my research statement.
T. Gillespie, P. Samanta, Y. Ye, Double Square Moments and Bounds for Resonance Sums of Cusp Forms
https://doi.org/10.1016/j.jnt.2022.11.012
S. Haag, P. Samanta, Swati, H. Swisher, S. Treneer, R. Visser, Repellent Properties of Perfect Powers on Partition Functions: A Heuristic Approach
Accepted for Publication at Research in the Mathematical Sciences
https://doi.org/10.48550/arXiv.2601.18138
C. Balz, P. Samanta, Mixed Spectral Second Moments of Rankin–Selberg L-functions
Preprint in Preparation
(Upcoming) Mathematics Colloquium at the University of Iowa, Fall 2026
Resonance Sums, Shifted Convolutions, and Bounds towards the Square-Root Cancellation Hypothesis, Algebra and Combinatorics Seminar, Tulane University, March 2026
Resonance Sums, Shifted Convolutions, and Bounds towards the Square-Root Cancellation Hypothesis, Algebra and Number Theory Seminar (virtual), Oregon State University, October 2025
Partition Functions and Perfect Powers, Speed TORA, Texas-Oklahoma Representations and Automorphic Forms, University of Oklahoma, April 2026
Double Square Moments & Bounds for Resonance Sums of Cusp Forms, AMS Contributed Paper Session in Number Theory and Field Theory I, Joint Mathematics Meetings, 2023
Double Square Moments and Bounds for Resonance Sums of Cusp Forms, Quebec-Maine Number Theory Conference, Laval University, October 2022
Double Square Moments and Bounds for Resonance Sums of Cusp Forms, Texas-Oklahoma Representations and Automorphic forms, Oklahoma State University, April 2022
Double Square Moments & Bounds for Resonance Sums for Cusp Forms, 34th Automorphic Forms Workshop (virtual) 2022
Double Square Moments & Bounds for Resonance Sums for Cusp Forms, TORA, Oklahoma State University, 2002
Picard’s Little Theorem, Conference on the Birch and Swinnerton-Dyer Conjecture, ICTS-TIFR, 2017
All talks are between Fall 2017 - 2023 at the University of Iowa
Bounds Towards Hypothesis S, Graduate and Undergraduate Students Seminar
Rankin Selberg Convolution, Representation Theory Seminar
n-Level Correlation of non-trivial Zeros of L-Functions, Representation Theory Seminar
Explicit Formula for L-Functions, Representation Theory Seminar