与狄利克雷l函数有关的和的显式公式

Brahim Mittou
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引用次数: 0

摘要

设$p\geq3$为质数,设$m, n$和$l$为整数,设$\gcd(l,p)=1$为整数。设$\chi$为狄利克雷字符模$p$, $L(s,\chi)$为对应$\chi$的狄利克雷l函数。本文利用特征和和伯努利多项式的性质,给出了:$$\dfrac{2}{p-1} \sum \limits\sb{\underset{\chi(-1)=+1}{\chi\hspace{-0.2cm} \mod p}} \chi(l) L(m,\chi)L(n,\overline{\chi}) \text{ and }\dfrac{2}{p-1} \sum \limits\sb{\underset{\chi(-1)=-1}{\chi\hspace{-0.2cm} \mod p}} \chi(l) L(m,\chi)L(n,\overline{\chi})$$的显式表达式。
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Explicit formulas for sums related to Dirichlet L-functions
Let $p\geq3$ be a prime number and let $m, n$ and $l$ be integers with $\gcd(l,p)=1$. Let $\chi$ be a Dirichlet character modulo $p$ and $L(s,\chi)$ be the Dirichlet L-function corresponding to $\chi$. Explicit formulas for: $$\dfrac{2}{p-1} \sum \limits\sb{\underset{\chi(-1)=+1}{\chi\hspace{-0.2cm} \mod p}} \chi(l) L(m,\chi)L(n,\overline{\chi}) \text{ and }\dfrac{2}{p-1} \sum \limits\sb{\underset{\chi(-1)=-1}{\chi\hspace{-0.2cm} \mod p}} \chi(l) L(m,\chi)L(n,\overline{\chi})$$ are given in this paper by using the properties of character sums and Bernoulli polynomials.
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