2 citations · 4 across the 8 of their papers we have counts for
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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…