Vinogradov's Conjecture and Beyond

Shivarajkumar

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arXiv · 2111.05219

Vinogradov's Conjecture and Beyond

Shivarajkumar

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Abstract

In this paper, if prime $p\equiv 3\pmod 4$ is sufficiently large then we prove an upper bound on the number of occurences of any arbitrary pattern of quadratic residues and nonresidues of length $k$ as $k$ tends to $\lceil \log_2 p\rceil$. As an immediate consequence, it proves that, there exist a constant $c$ such that, the least nonresidue for such primes is at most $c\lceil \log_2 p\rceil$.

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Shivarajkumar. 2021-11-09. Vinogradov's Conjecture and Beyond. https://arxiv.org/abs/2111.05219

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