Number Theory

    

A Convergent Subsequence of $theta_n(x+iy)$ in a Half Strip

Authors: Young Deuk Kim

For $frac{1}{2}0$ and $ninmathbb{N}$, let $displaystyletheta_n(x+iy)=sum_{i=1}^nfrac{{mbox{sgn}}, q_i}{q_i^{x+iy}}$,where $Q={q_1,q_2,q_3,cdots}$ is the set of finite product of distinct odd primes and${mbox{sgn}}, q=(-1)^k$ if $q$ is the product of $k$ distinct primes.In this paper we prove that there exists an ordering on $Q$ such that $theta_n(x+iy)$ has a convergent subsequence.

Comments: 8 Pages. Typos are fixed.

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Submission history

[v1] 2024-01-14 20:59:31
[v2] 2024-01-19 20:47:42

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