PreprintCC BY 4.0arXiv
Primes and the Möbius function over quadratic polynomials
Abstract
We prove an asymptotic formula for the number of primes p≤ X of the form n2+h for almost all h ≤ X1/2−o(1). We prove that, for almost all h ≤ X2/5, the number of primes satisfies a correct-order lower bound. We also show cancellation of the Möbius function over n2+h for almost all h < X1/2−o(1).
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BibTeX
@misc{grimmelt2026primes,
title = {{Primes and the Möbius function over quadratic polynomials}},
author = {Lasse Grimmelt and Jori Merikoski and Mayank Pandey and Alexandru Pascadi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41356},
eprint = {2610.41356},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41356},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Primes and the Möbius function over quadratic polynomials
AU - Lasse Grimmelt
AU - Jori Merikoski
AU - Mayank Pandey
AU - Alexandru Pascadi
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41356
UR - https://arxiv.org/abs/2610.41356
AB - We prove an asymptotic formula for the number of primes p≤ X of the form n^2+h for almost all h ≤ X^1/2−o(1). We prove that, for almost all h ≤ X^2/5, the number of primes satisfies a correct-order lower bound. We also show cancellation of the Möbius function over n^2+h for almost all h < X^1/2−o(1).
ER -