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arXiv · 2610.41356

Primes and the Möbius function over quadratic polynomials

Lasse Grimmelt·Jori Merikoski·Mayank Pandey·Alexandru Pascadi
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Abstract

We prove an asymptotic formula for the number of primes $p\leq X$ of the form $n^2+h$ for almost all $h \leq X^{1/2-o(1)}$. We prove that, for almost all $h \leq X^{2/5}$, 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 $h < X^{1/2-o(1)}$.

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Lasse Grimmelt, Jori Merikoski, Mayank Pandey, Alexandru Pascadi. 2026-10-30. Primes and the Möbius function over quadratic polynomials. https://arxiv.org/abs/2610.41356

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