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Mertens conjecture
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==Further reading== * {{cite conference |title=The Mertens Conjecture Revisited | first1=Tadej | last1=Kotnik | first2=Herman | last2=te Riele | author2-link=Herman te Riele | year= 2006 | series=Lecture Notes in Computer Science | volume=4076 | publisher=[[Springer-Verlag]] | book-title=Algorithmic number theory. 7th international symposium, ANTS-VII, Berlin, Germany, July 23--28, 2006. Proceedings | editor1-last=Hess | editor1-first=Florian | pages=156–167 | location=Berlin | doi=10.1007/11792086_12 | zbl=1143.11345 | isbn=3-540-36075-1 }} * {{cite journal | last1 = Kotnik | first1 = T. | last2 = van de Lune | first2 = J. | year = 2004 | title = On the order of the Mertens function | url = http://www.expmath.org/expmath/volumes/13/13.4/Kotnik.pdf | journal = Experimental Mathematics | volume = 13 | issue = 4 | pages = 473–481 | doi = 10.1080/10586458.2004.10504556 | s2cid = 2093469 | url-status = dead | archive-url = https://web.archive.org/web/20070403143340/http://expmath.org/expmath/volumes/13/13.4/Kotnik.pdf | archive-date = 2007-04-03 }} * {{cite journal | last1 = Mertens | first1 = F. | year = 1897 | title = Über eine zahlentheoretische Funktion | journal = Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Klasse, Abteilung 2a | volume = 106 | pages = 761–830 }} * {{Citation | last1=Odlyzko | first1=A. M. | author1-link=Andrew Odlyzko | last2=te Riele | first2=H. J. J. | author2-link=Herman te Riele | title=Disproof of the Mertens conjecture | url=http://www.dtc.umn.edu/~odlyzko/doc/arch/mertens.disproof.pdf | doi=10.1515/crll.1985.357.138 |mr=783538 | year=1985 | journal=[[Journal für die reine und angewandte Mathematik]] | volume=1985 | issue=357 | pages=138–160 | zbl=0544.10047 | s2cid=13016831 | issn=0075-4102 }} * {{cite journal | last1 = Pintz | first1 = J. | year = 1987 | title = An effective disproof of the Mertens conjecture | url = http://www.numdam.org/article/AST_1987__147-148__325_0.pdf | journal = [[Astérisque]] | volume = 147–148 | pages = 325–333 | zbl=0623.10031 }} * {{citation | editor1-last=Sándor | editor1-first=József | editor2-last=Mitrinović | editor2-first=Dragoslav S. | editor3-last=Crstici |editor3-first=Borislav | title=Handbook of number theory I | location=Dordrecht | publisher=[[Springer-Verlag]] | year=2006 | isbn=1-4020-4215-9 | zbl=1151.11300 | pages=187–189 }} *{{citation|first= T. J.|last= Stieltjes|chapter= Lettre a Hermite de 11 juillet 1885, Lettre #79|pages= 160–164 |editor-first=B.|editor-last= Baillaud |editor2-first= H.|editor2-last= Bourget|title=Correspondance d'Hermite et Stieltjes|place= Paris|publisher= Gauthier—Villars|year= 1905}} * {{mathworld|urlname=MertensConjecture|title=Mertens conjecture}}
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