Matches in SemOpenAlex for { <https://semopenalex.org/work/W2798833335> ?p ?o ?g. }
Showing items 1 to 66 of
66
with 100 items per page.
- W2798833335 abstract "Let $P$ be the set of all prime numbers, ${q_1},{q_2}, cdots ,{q_m} in P$, $P_k$ be the k-th $(k = 1,2, cdots m)$ element of $P$ in ascending order of size, ${alpha _1},{alpha _2}, cdots ,{alpha _m}$ be positive integers, and ${beta _1},{beta _2}, cdots ,{beta _m}$ is a permutation of ${alpha _1},{alpha _2}, cdots ,{alpha _m}$ with ${beta _1} ge {beta _2} ge cdots ge {beta _m}$, The following results are given in this paper: (i) The following inequality is true: ${e^gamma }log log prodlimits_{k = 1}^m {q_k^{alpha _k}} - prodlimits_{k = 1}^m {frac{{{q_k} - {textstyle{1 over {q_k^{alpha _k}}}}}}{{{q_k} - 1}}} ge {e^gamma }log log prodlimits_{k = 1}^m {p_k^{beta _k}} - prodlimits_{k = 1}^m {frac{{{p_k} - {textstyle{1 over {p_k^{beta _k}}}}}}{{{p_k} - 1}}}$. (ii) If $n = prodlimits_{k = 1}^m {p_k^{beta _k}}= {left( {prodlimits_{k = 1}^m {p_k} } right)^{1 + {varepsilon _m}(n)}}$, $mathop {lim }limits_{m to infty } {varepsilon _m}(n) > 0$ or $mathop {lim }limits_{m to infty } {varepsilon _m}(n) = + infty$, then $mathop {lim }limits_{m to infty } ({e^gamma }nlog log n - sigma (n)) > 0$ . Where ${ {beta _k}}$ is a sequence, ${beta _k} in N$, ${beta _1} ge {beta _2} ge cdots ge {beta _m}$, $sigma (n) = sumlimits_{left. d right|n} d$, and $gamma$ is the Euler constant. (iii) The probability of Riemann's hypothesis being true is equal to 1. In addition, two results are given when $mathop {lim }limits_{m to infty } {varepsilon _m}(n) = 0$." @default.
- W2798833335 created "2018-05-07" @default.
- W2798833335 creator A5005938550 @default.
- W2798833335 date "2016-09-24" @default.
- W2798833335 modified "2023-09-27" @default.
- W2798833335 title "The probability of Riemann's hypothesis being true is equal to 1" @default.
- W2798833335 cites W1480319329 @default.
- W2798833335 cites W1512645620 @default.
- W2798833335 cites W1581351779 @default.
- W2798833335 cites W1979858219 @default.
- W2798833335 cites W1991057622 @default.
- W2798833335 cites W2047087993 @default.
- W2798833335 cites W2052074787 @default.
- W2798833335 cites W2101718938 @default.
- W2798833335 cites W2137308309 @default.
- W2798833335 cites W2152890878 @default.
- W2798833335 cites W2242225202 @default.
- W2798833335 cites W2282130622 @default.
- W2798833335 cites W2741003235 @default.
- W2798833335 cites W2986262373 @default.
- W2798833335 cites W3013127871 @default.
- W2798833335 cites W3169277 @default.
- W2798833335 cites W347294826 @default.
- W2798833335 hasPublicationYear "2016" @default.
- W2798833335 type Work @default.
- W2798833335 sameAs 2798833335 @default.
- W2798833335 citedByCount "0" @default.
- W2798833335 crossrefType "posted-content" @default.
- W2798833335 hasAuthorship W2798833335A5005938550 @default.
- W2798833335 hasConcept C10138342 @default.
- W2798833335 hasConcept C114614502 @default.
- W2798833335 hasConcept C162324750 @default.
- W2798833335 hasConcept C182306322 @default.
- W2798833335 hasConcept C33923547 @default.
- W2798833335 hasConceptScore W2798833335C10138342 @default.
- W2798833335 hasConceptScore W2798833335C114614502 @default.
- W2798833335 hasConceptScore W2798833335C162324750 @default.
- W2798833335 hasConceptScore W2798833335C182306322 @default.
- W2798833335 hasConceptScore W2798833335C33923547 @default.
- W2798833335 hasLocation W27988333351 @default.
- W2798833335 hasOpenAccess W2798833335 @default.
- W2798833335 hasPrimaryLocation W27988333351 @default.
- W2798833335 hasRelatedWork W1608924249 @default.
- W2798833335 hasRelatedWork W1794769192 @default.
- W2798833335 hasRelatedWork W1989006314 @default.
- W2798833335 hasRelatedWork W2039948047 @default.
- W2798833335 hasRelatedWork W2170003428 @default.
- W2798833335 hasRelatedWork W2170363454 @default.
- W2798833335 hasRelatedWork W22122152 @default.
- W2798833335 hasRelatedWork W2316215935 @default.
- W2798833335 hasRelatedWork W2317664832 @default.
- W2798833335 hasRelatedWork W2491485826 @default.
- W2798833335 hasRelatedWork W2531614474 @default.
- W2798833335 hasRelatedWork W2765777434 @default.
- W2798833335 hasRelatedWork W2907135717 @default.
- W2798833335 hasRelatedWork W2949092878 @default.
- W2798833335 hasRelatedWork W2950509301 @default.
- W2798833335 hasRelatedWork W2950856764 @default.
- W2798833335 hasRelatedWork W2952586717 @default.
- W2798833335 hasRelatedWork W2953278774 @default.
- W2798833335 hasRelatedWork W2966062710 @default.
- W2798833335 hasRelatedWork W3107606979 @default.
- W2798833335 isParatext "false" @default.
- W2798833335 isRetracted "false" @default.
- W2798833335 magId "2798833335" @default.
- W2798833335 workType "article" @default.