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    Scientists / Open questions

    詹姆斯·梅纳德

    James Maynard

    解析数论、素数分布

    2022 年菲尔兹奖

    9 个问题

    1. Completely uniform distribution of primes to moduli x1/2+δx^{1/2+\delta}: the balanced Type II estimate, the four-factor terms, and the full extension of Bombieri–Vinogradov

    2. The constant-2 Brun–Titchmarsh theorem below x≥q8x \ge q^8: widening the admissible range for general moduli

    3. Polynomial degree dependence and explicit k-dependence in simultaneous small fractional parts of polynomials

    4. The true quantitative range of primes and polynomial values with restricted digits: minimal base, digit-exclusion density, polynomial-degree dependence, and effective error terms

    5. Cilleruelo's conjecture on the least common multiple of polynomial sequences

    6. The maximal well-factorable level of distribution of primes in arithmetic progressions

    7. Primes with restricted decimal digits: the asymptotic formula for one excluded digit and the existence of primes avoiding two digits in base 10

    8. Asymptotic formulae for primes represented by incomplete norm forms below the n≥4kn \ge 4k barrier

    9. Dense clusters of primes in short intervals and Chebotarev sets: uniformity in the cluster size m and distribution estimates with exponential log-scale savings

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