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105 papers · 1 filter
On Triple Quadratic Residue Symbols in Real Quadratic Fields
Atsuki Kuramoto
We introduce triple quadratic residue symbols for certain finite primes 's of a real quadratic field with tri…
On finite analogues of Euler's constant
Masanobu Kaneko, Toshiki Matsusaka, Shin-ichiro Seki
We introduce and study finite analogues of Euler's constant in the same setting as finite multiple zeta values. We define a couple of candidate values from the perspectives of a ``…
On a smoothed average of the number of Goldbach representations
Daniel A. Goldston, Ade Irma Suriajaya
Assuming the Generalized Riemann Hypothesis for the zeros of the Dirichlet -functions with characters modulo , we obtain a smoothed version of the average number of Goldbach…
An unconditional Montgomery Theorem for Pair Correlation of Zeros of the Riemann Zeta Function
Siegfred Alan C. Baluyot, Daniel Alan Goldston, Ade Irma Suriajaya +1
Assuming the Riemann Hypothesis (RH), Montgomery proved a theorem concerning pair correlation of zeros of the Riemann zeta-function. One consequence of this theorem is that, assumi…
The Average Number of Goldbach Representations and Zero-Free Regions of the Riemann Zeta-Function
Keith Billington, Maddie Cheng, Jordan Schettler +1
In this paper, we prove an unconditional form of Fujii's formula for the average number of Goldbach representations and show that the error in this formula is determined by a gener…
The Prime Number Theorem and Pair Correlation of Zeros of the Riemann Zeta-Function
D. A. Goldston, Ade Irma Suriajaya
We prove that the error in the prime number theorem can be quantitatively improved beyond the Riemann Hypothesis bound by using versions of Montgomery's conjecture for the pair cor…