On a generalization of Polya inequality and some of its statistical implications
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摘要
Let p be a prime and χ a nonprincipal character modp. Let 1⩽m⩽p and l an integer so that p∤l. Then, we have |∑a=0m−1χ(a)χ(a+l)|⩽3plnp. The proof makes use of estimation on Kloosterman sum via the Riemann hypothesis on finite fields. As simple consequence of the theorem we obtain a uniform distribution of consecutive quadratic residues modp.
论文关键词:Character,Gauss sum,Kloosterman sum,Quadratic residue,Distribution,Legendre symbol,Riemann hypothesis on finite fields
论文评审过程:Received 5 October 2000, Revised 23 April 2001, Available online 9 April 2002.
论文官网地址:https://doi.org/10.1016/S0377-0427(01)00459-9