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papers

Publications (4)

math.NT2022

Double square moments and bounds for resonance sums of cusp forms

Tim Gillespie, Praneel Samanta, Yangbo Ye

Let $f$ and $g$ be holomorphic cusp forms for the modular group $S L_{2} (Z)$ of weight $k_{1}$ and $k_{2}$ with Fourier coefficients $I^»_{f} (n)$ and $I^»_{g} (n)$ , respectively. For rea…

math.NT2009

Solvable Base Change and Rankin-Selberg Convolutions

Tim Gillespie

Given unitary automorphic cuspidal representations $I ¨ $ and $I ¨ ^{'}$ defined on $G L_{n} (A_{E})$ and $G L_{m} (A_{F})$ , respectively, with $E$ and $F$ solvable algebraic number…

physics.optics2025

Detectorless 3D terahertz imaging: achieving subwavelength resolution with reflectance confocal interferometric microscopy

Jorge Silva, Martin PlÃ¶schner, Karl Bertling +18

Terahertz imaging holds great potential for non-destructive material inspection, but practical implementation has been limited by resolution constraints. In this study, we present…

math.NT2009

A Prime Number Theorem for Rankin-Selberg L-functions over Number fields

Tim Gillespie, Guanghua Ji

We prove a prime number theorem first for the classical Rankin-Selberg L-function $L (s, I ¨ \times I ¨ ^{'})$ over any Galois extension with $I ¨ $ and $I ¨ ^{'}$ unitary automorphic cuspidal repr…