Mike Swarbrick Jones
We generalise a result of Heath-Brown and Skorobogatov to show that a certain class of varieties over a number field $k$ satisfies Weak Approximation and the Hasse Principle, provided there is no Brauer-Manin obstruction.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Let $χ$ a primitive character$\pmod q$ and consider the Dirichlet $L$-function $$L(s,χ)=\sum_{n=1}^{\infty}\frac{χ(n)}{n^s}.$$ We give a new proof of an upper bound of Heath-Brown for $|L(s,χ)|$ on the critical line $s=1/2+it$
Jacob's ladders, new equivalent of the Fermat-Wiles theorem generated by certain cross-breed of Ingham and Heath-Brown formula (1979) and some chains of equivalents
本文基于Ingham与Heath-Brown公式的混合形式，证明了Fermat-Wiles定理的一个新等价形式，并证明了一类数学分析等价表达式的有限链存在无限集合。
Zero-free regions inspired by work of Heath-Brown
基于Heath-Brown的工作，论文证明了黎曼ζ函数在特定区域无零点，提出新的显式无零区域并验证了σ≥1-1/(4.896logt)时ζ(σ+it)≠0。
A survey of moment bounds for $ζ(s)$: from Heath Brown's work to the present
本文综述了Heath-Brown关于Riemann zeta函数矩界的工作及其影响，并总结了近期结果，这些结果在无条件或Riemann假设下恢复了所有矩的预期增长速率。
In his paper from 1996 on quadratic forms Heath-Brown developed a version of circle method to count points in the intersection of an unbounded quadric with a lattice of short period, if each point is given a weight. The weight function is assumed to be $C_0^\infty$-smooth and to vanish near the singularity of the quadric. In out work we allow the weight function to be finitely smooth and not vanish near the singularity, and we give also an explicit dependence on the weight function.
Let a and q be coprime natural numbers. In 1944 Linnik proved that the least prime in an arithmetic progression a mod q is less then C times q to the L. Since then the admissible value for the constant L has been improved several times, lastly by Heath-Brown in 1992 to L=5.5. In his article Heath-Brown describes several improvement potentials for his paper. Using these potentials we improve the intermediate results concerning zeros of Dirichlet L-Functions and finally the admissible constant to L=5.2. ----- Seien a und q teilerfremde natuerliche Zahlen. 1944 bewies Linnik, dass die kleinste Pr…
We study lower bound estimates for the number of solutions of systems of equations over finite fields. Heath-Brown improved the lower bounds given by the classical \emph{Chevalley-Warning Theorems} by excluding systems of equations whose solutions form an affine space. We improve each of Heath-Brown's results and demonstrate sharpness in several cases.
A refinement of Heath-Brown's theorem on quadratic forms
本文改进了Heath-Brown 1996年关于二次型的定理，放宽了权重函数的光滑度要求，允许其在奇点处不消失并在无穷远处显式衰减，且仅用初等数论结果推导。
Binary linear forms as sums of two squares
我们重新回顾Heath-Brown最近关于量r（L_1）r（L_2）r（L_3）r（L_4）的平均阶的工作，对于适当的二元线性型L_1，.，L_4，对于在相当一般的区域范围内的整数。除了改进希思-布朗估计的误差项外，我们还相当广泛地推广了他的结果。
On the mean square gap between primes
该数学论文改进了连续素数差平方平均值的上界，采用Harman筛法等工具，将Peck的O(x^{0.25+ε})界优化为O(x^{0.23+ε})。
Heath-Brown identities for fractional powers of $ζ$
该研究构造了黎曼ζ函数分数次幂的希思-布朗型恒等式，证明了相关指数和的维诺格拉多夫级界，确定了一类和函数的主弧展开、量级及矩的渐近公式，次弧分析避开了L-函数理论。
Let $Q$ be a nondegenerate quadratic form on a vector space $V$ of even dimension $n$ over a number field $F$. Via the circle method or automorphic methods one can give good estimates for smoothed sums over the number of zeros of the quadratic form whose coordinates are of size at most $X$ (properly interpreted). For example, when $F=\mathbb{Q}$ and $\dim V>4$ Heath-Brown has given an asymptotic of the form \begin{align} \label{HB:esti} c_1X^{n-2}+O_{Q,\varepsilon,f}(X^{n/2+\varepsilon}) \end{align} for any $\varepsilon>0$. Here $c_1 \in \mathbb{C}$ and $f \in \mathcal{S}(V(\mathbb{R}))$ is a …
We give a short alternative proof using Heath-Brown's square sieve of a bound of the author for the large sieve with square moduli.
The fourth moment of Dirichlet $L$-functions
推广Heath-Brown的一个结果，建立了附着在本原特征标$\pmod q$上的Dirichlet $L$ -函数中心值四阶矩的一个渐近公式.
We prove an analogue of Heath-Brown's bound on the twelfth moment of the Riemann zeta function for Dirichlet L-functions with smooth moduli.
Improving on a theorem of Heath-Brown, we show that if $X$ is sufficiently large then a positive proportion of the values $\{n^3+2:n\in (X,2X]\}$ have a prime factor larger than $X^{1+10^{-52}}$.
Explicit quadratic large sieve inequality
本文得到了Heath-Brown二次特征大筛不等式的显式版本，并讨论了其在L-函数和二次域中的应用。
We prove a modification as well as an improvement of a result of K. Ford, D. R. Heath-Brown and S. Konyagin concerning prime avoidance of square-free numbers and perfect powers of prime numbers.
Carmichael Numbers with Prime Numbers of Prime Factors
本文在Heath-Brown猜想下，证明了存在无穷多个Carmichael数，其素因子个数为素数。
We establish an analogue of a conjecture of Balasubramanian, Conrey, and Heath-Brown for the family of all Dirichlet characters with conductor up to $Q$. This forms another application of our work in developing an asymptotic large sieve.
On moments of L-functions over Dirichlet characters
本文为Dirichlet L-函数二阶矩的Heath-Brown完整渐近展开提供了新证明，并将相应渐近展开推广到Hecke-Maass L-函数的扭曲一阶矩。
Special cubic zeros and the dual variety
本文基于对偶簇和 delta 方法，无条件提取了 $6$ 变量对角三次型特殊整零点的加权和，并提出了适用于更一般情况的公理化框架。
We employ a generalised version of Heath-Brown's square sieve in order to establish an asymptotic estimate of the number of solutions $a, b \in \mathbb N$ to the equations $a+b=n$ and $a-b=n$, where $a$ is $k$-free and $b$ is $l$-free. This is the first time that this problem has been studied with distinct powers $k$ and $l$.
We address Heath-Brown's and Serre's dimension growth conjecture (proved by Salberger), when the degree $d$ grows. Recall that Salberger's dimension growth results give bounds of the form $O_{X, \varepsilon} (B^{\dim X+\varepsilon})$ for the number of rational points of height at most $B$ on any integral subvariety $X$ of ${\mathbb P}^n_{\mathbb Q}$ of degree $d\geq 2$, where one can write $O_{d,n, \varepsilon}$ instead of $O_{X, \varepsilon}$ as soon as $d\geq 4$. Our main contribution is to remove the factor $B^\varepsilon$ as soon as $d \geq 5$, without introducing a factor $\log B$, while …
We prove the q-aspect analogue of Heath-Brown's result on the twelfth power moment of the Riemann zeta function for Dirichlet L-functions to odd prime power moduli. Our results rely on the p-adic method of stationary phase for sums of products and complement Nunes' bound for smooth square-free moduli.
Counting integer points on affine surfaces with a side condition
本研究基于行列式法拓展前人工作，给出带多项式同余条件的有界高度仿射曲面整数点的一致上界，并将其应用于对角二次曲面点计数及四异幂和整数表示问题。
The largest prime factor of an irreducible cubic polynomial
将Heath-Brown关于$n^3+2$存在大于$n^{1+c}$的素因子的结论推广到任意首一不可约三次整系数多项式，并给出依赖于多项式的指数$c_p$。
We generalise the square sieve developed by Heath-Brown to higher powers in order to improve on the error term for the problem of counting consecutive power-free numbers.
We use a global version of Heath-Brown's $p-$adic determinant method developed by Salberger to give upper bounds for the number of rational points of height at most $B$ on non-singular cubic curves defined over $\mathbb{Q}$. The bounds are uniform in the sense that they only depend on the rank of the corresponding Jacobian.
Limiting Distribution and Rate of Convergence for GL(3) Fourier Coefficients
本文研究了GL(3)傅里叶系数的极限分布及其收敛速度，通过证明在GL(3)设定下，归一化误差项的分布函数存在，并给出了极限分布的定量收敛速度。
We extend the work of Salberger; Walsh; Castryck, Cluckers, Dittmann and Nguyen; and Vermeulen to prove the uniform dimension growth conjecture of Heath-Brown and Serre for varieties of degree at least $4$ over global fields. As an intermediate step, we generalize the bounds of Bombieri and Pila to curves over global fields and in doing so we improve the $B^{\varepsilon}$ factor by a $\log(B)$ factor.
Slope-determinant method, complex cellular structures and hypersurface coverings of regular rational points
本文结合 Bombieri-Pila/Heath-Brown 行列式方法、Chen 的 Arakelov 斜率重构与 Binyamini-Novikov 复细胞结构，将正则有理点超曲面覆盖计数中的次多项式因子改进为多对数因子。
A note on zero-density approaches for the difference between consecutive primes
本研究推广了短区间素数相关的Ingham定理与Heath-Brown和Iwaniec的结果，明晰了无零点区域、零密度估计和短区间素数的关联，还在密度假设下改进了素数定理成立的短区间范围。
The prime number theorem over integers of power-free polynomial values
本文基于Bergelson和Richter的工作，研究了多项式幂自由整数的素数定理变体，探讨了其在Estermann等研究的多项式上的应用。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。