5 citations · 6 across the 6 of their papers we have counts for
7 papers
A translation of N.M. Katz's "Exponential Sums"
David T. Nguyen
These notes are devoted to the theory of exponential sums over finite fields. The first chapter recalls some of the number-theoretic interest of such sums. The second chapter discu…
Generalized divisor functions in arithmetic progressions: I
David T. Nguyen
We prove some distribution results for the -fold divisor function in arithmetic progressions to moduli that exceed the square-root of length of the sum, with appropriate con…
On Ramanujan-Fourier expansions
David T. Nguyen
We heuristically study the shifted convolution using a normalized version of Ramanujan-Fourier expansions for and verify they produce th…
A note on
David Nguyen
It is a classic result of Selberg in the 1950's that , where is the level of distribution of the divisor function in arithmetic progressions (defined more precisel…
On correlation of the 3-fold divisor function with itself
David T. Nguyen
Let . We present three conditional results on the ternary additive correlation sum $$\sum_{n\le X} τ_3(n) τ_3(n+h),\quad (h\ge…
Variance of the k-fold divisor function in arithmetic progressions for individual modulus
David T. Nguyen
In this paper, we confirm a smoothed version of a recent conjecture on the variance of the k-fold divisor function in arithmetic progressions to individual composite moduli, in a r…
Explicit formulas for enumeration of lattice paths: basketball and the kernel method
Cyril Banderier, Christian Krattenthaler, Alan Krinik +4
This article deals with the enumeration of directed lattice walks on the integers with any finite set of steps, starting at a given altitude and ending at a given altitude ,…