In classical prime number theory there are several asymptotic formulas said to be “equivalent” to the PNT. One is the bound
Dans la théorie des nombres premiers classique, certaines expressions sont considérées comme « équivalentes » au TNP (Théorème des nombres premiers). Parmi elles on trouve la borne
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DOI : 10.5802/jtnb.1034
Mots-clés : Beurling generalized numbers; mean-value vanishing of the Moebius function; Chebyshev bounds; zeta function; prime number theorem; PNT equivalences
Gregory Debruyne 1 ; Harold G. Diamond 2 ; Jasson Vindas 1

@article{JTNB_2018__30_2_469_0, author = {Gregory Debruyne and Harold G. Diamond and Jasson Vindas}, title = {$M(x)=o(x)$ {Estimates} for {Beurling} numbers}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {469--483}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {30}, number = {2}, year = {2018}, doi = {10.5802/jtnb.1034}, zbl = {1443.11201}, mrnumber = {3891322}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1034/} }
TY - JOUR AU - Gregory Debruyne AU - Harold G. Diamond AU - Jasson Vindas TI - $M(x)=o(x)$ Estimates for Beurling numbers JO - Journal de théorie des nombres de Bordeaux PY - 2018 SP - 469 EP - 483 VL - 30 IS - 2 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1034/ DO - 10.5802/jtnb.1034 LA - en ID - JTNB_2018__30_2_469_0 ER -
%0 Journal Article %A Gregory Debruyne %A Harold G. Diamond %A Jasson Vindas %T $M(x)=o(x)$ Estimates for Beurling numbers %J Journal de théorie des nombres de Bordeaux %D 2018 %P 469-483 %V 30 %N 2 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1034/ %R 10.5802/jtnb.1034 %G en %F JTNB_2018__30_2_469_0
Gregory Debruyne; Harold G. Diamond; Jasson Vindas. $M(x)=o(x)$ Estimates for Beurling numbers. Journal de théorie des nombres de Bordeaux, Tome 30 (2018) no. 2, pp. 469-483. doi : 10.5802/jtnb.1034. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1034/
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- On the estimate
for Beurling generalized numbers, Analysis Mathematica, Volume 50 (2024) no. 4, pp. 1131-1140 | DOI:10.1007/s10476-024-00061-6 | Zbl:7966650 - Oscillation of the Remainder Term in the Prime Number Theorem of Beurling, “Caused by a Given ζ-Zero”, International Mathematics Research Notices, Volume 2023 (2023) no. 14, p. 11752 | DOI:10.1093/imrn/rnac274
- Halász's theorem for Beurling generalized numbers, Acta Arithmetica, Volume 194 (2020) no. 1, pp. 59-72 | DOI:10.4064/aa190210-22-5 | Zbl:1462.11074
- Beurling numbers whose number of prime factors lies in a specified residue class, Acta Arithmetica, Volume 196 (2020) no. 4, pp. 433-438 | DOI:10.4064/aa200130-15-6 | Zbl:1465.11191
- The average order of the Möbius function for Beurling primes, International Journal of Number Theory, Volume 16 (2020) no. 5, pp. 1005-1011 | DOI:10.1142/s1793042120500517 | Zbl:1475.11180
- On Diamond's
criterion for asymptotic density of Beurling generalized integers, Michigan Mathematical Journal, Volume 68 (2019) no. 1, pp. 211-223 | DOI:10.1307/mmj/1548903624 | Zbl:1465.11195 - Halász's theorem for Beurling numbers, Acta Arithmetica, Volume 183 (2018) no. 3, pp. 223-235 | DOI:10.4064/aa8668-11-2017 | Zbl:1422.11202
- Prime number theorem equivalences and non-equivalences, Mathematika, Volume 63 (2017) no. 3, pp. 852-862 | DOI:10.1112/s0025579317000201 | Zbl:1426.11116
Cité par 8 documents. Sources : Crossref, zbMATH