Arithmetic exponent pairs for algebraic trace functions and applications
Arithmetic exponent pairs for algebraic trace functions and applications
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DOI：
10.2140/ant.2021.15.2123
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发表时间：
2016-03
影响因子：
1.3
通讯作者：
Jie Wu;Ping Xi
中科院分区：
文献类型：
--
作者：
Jie Wu;Ping Xi
本文利用vandercorput方法的$q$ -类比方法研究了代数迹函数的短和，并在模具有足够好的分解性的情况下，提出了与经典情况相符的算术指数对方法。作为应用，我们平均证明了brn - titchmarsh定理的二次模拟，用$p^2+1\equiv0\pmod q$限定质数$p\leqslant X$的个数。其他两个应用包括等差数列中除数函数的更大程度的分布和Dirichlet的子weyl次凸界$L$ -函数先前由Irving研究过。
We study short sums of algebraic trace functions via the $q$-analogue of van der Corput method, and develop methods of arithmetic exponent pairs that coincide with the classical case while the moduli has sufficiently good factorizations. As an application, we prove a quadratic analogue of Brun-Titchmarsh theorem on average, bounding the number of primes $p\leqslant X$ with $p^2+1\equiv0\pmod q$. The other two applications include a larger level of distribution of divisor functions in arithmetic progressions and a sub-Weyl subconvex bound of Dirichlet $L$-functions studied previously by Irving.