2 citations · 4 across the 8 of their papers we have counts for
8 papers
A Subconvex Metaplectic Prime Geodesic Theorem and the Shimura Correspondence
Ikuya Kaneko
We investigate the prime geodesic theorem with an error term dependent on the varying weight and its higher metaplectic coverings in the arithmetic setting, each admitting subconve…
The Prime Geodesic Theorem and Bounds for Character Sums
Ikuya Kaneko
We establish the prime geodesic theorem for the modular surface with exponent , improving upon the long-standing exponent of So…
The Prime Geodesic Theorem for the Picard Orbifold
Ikuya Kaneko
We establish the prime geodesic theorem for the Picard orbifold , wherein the error term shrinks proportionally to improv…
On a Finite Field Analogue of van der Corput Differencing
Ikuya Kaneko
We establish nontrivial bounds for general bilinear forms with a given periodic function, which are thought of as an analogue of van der Corput differencing for exponential sums. T…
Non-Linear Additive Twists of Hecke Eigenvalues
Ikuya Kaneko, Wing Hong Leung
We bound non-linear additive twists of Hecke eigenvalues, improving upon the work of Kumar-Mallesham-Singh (2022). The proof employs the DFI circle method with st…
Mean Values and Quantum Variance for Degenerate Eisenstein Series of Higher Rank
Dimitrios Chatzakos, Corentin Darreye, Ikuya Kaneko
We investigate the mean value of the inner product of squared degenerate maximal parabolic Eisenstein series against a smooth compactly supported function lying i…
On Multiple Shifted Convolution Sums
Ikuya Kaneko
We prove strong estimates for averages of shifted convolution sums consisting of quadratic twists of -functions. The key input involves the circle method toget…
The Prime Geodesic Theorem in Arithmetic Progressions
Dimitrios Chatzakos, Gergely Harcos, Ikuya Kaneko
We address the prime geodesic theorem in arithmetic progressions, and resolve conjectures of Golovchanski\uı-Smotrov (1999). In particular, we prove that the traces of closed geode…