TL;DR
This paper studies the non-correlation of Fourier coefficients of Maass forms with oscillatory functions and proves an equidistribution result for twisted horocycles, advancing understanding of their distribution properties.
Contribution
It introduces new non-correlation results for Maass form coefficients against oscillatory functions and derives an equidistribution theorem for twisted horocycles.
Findings
Established non-correlation between Fourier coefficients and oscillatory functions.
Proved equidistribution of twisted horocycles.
Extended analogy with Frobenius trace function results.
Abstract
We investigate non-correlation of Fourier coefficients of Maass forms against a class of real oscillatory functions, in analogy to known results with Frobenius trace functions. We also establish an equidistribution result for twisted horocycles as a consequence of our non-correlation result.
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