8 papers
Security in LLM-Assisted Coding: A Systematic Literature Review
Liang Yuan, Maryam Khanian Najafabadi, Mashud Rana +1
Large Language Models accelerate software development but introduce severe security vulnerabilities. This systematic review investigates security risks in automated coding, benchma…
Zeros of the Dirichlet series of even zeta values
William D. Banks
We give a complete unconditional description of the zero set of the Dirichlet series , which continues meromorphically to w…
Unshared zeros of Dirichlet -functions
William Banks, Kyle Loftus
We prove that no Dirichlet -function (and more generally, no nontrivial finite linear combination of Dirichlet -functions) can vanish at every zero of a fixed . At…
The alien in the Riemann zeta function
William D. Banks
In space, no one can hear you scream.
Pair correlation for sums of two ordinates of zeros of the Riemann zeta function
William D. Banks
Assuming the Riemann Hypothesis, we extend Montgomery's pair correlation method to study the distribution of differences between sums of two ordinates of nontrivial zeros…
A variant of the Linnik-Sprindzuk theorem for simple zeros of Dirichlet L-functions
William D. Banks
For a primitive Dirichlet character , a new hypothesis is introduced, which asserts that (1) all simple zeros of in the critical strip are located…
Consecutive primes and IP sets
William D. Banks
For an infinite set M of natural numbers, let FS(M) be the set of all nonzero finite sums of distinct numbers in M. An IP set is any set of the form FS(M). Let p_n denote the n-th…
The Generalized Riemann Hypothesis from zeros of a single L-function
William D. Banks
For each primitive Dirichlet character , a hypothesis is formulated in terms of zeros of the associated -function . It is shown that for any su…