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In mathematics, the Mertens conjecture is the statement that the Mertens function M {\displaystyle M(n)} is bounded by ± n {\displaystyle \pm {\sqrt {n}}} . Although now disproven, it has been shown to imply the Riemann hypothesis.
In number theory, the Mertens function is defined for all positive integers n as M = ∑ k = 1 n μ ( k ) {\displaystyle M(n)=\sum _{k=1}^{n}\mu (k)} where μ(k) is the Möbius function. The function is named in honour of Franz Mertens.
Mertensia is a genus of flowering plants in the family Boraginaceae. They are perennial herbaceous plants with blue or sometimes white flowers that open from pink-tinged buds.
Mertensia virginica is a spring ephemeral plant with bell-shaped sky-blue flowers, native to eastern North America.
Mertens s]) is a Dutch-language patronymic surname, meaning "son of Merten" (Martin). It is the fifth most common name in Belgium with 18,518 people in 2008.
Mertens v. Hewitt Associates, 508 U.S. 248 , is the second in the trilogy of United States Supreme Court ERISA preemption cases that effectively denies any remedy for employees who are harmed by medical malpractice or other bad acts of their health plan if they receive their health care from their employer.
Mertens' water monitor , also called commonly Mertens's water monitor, and often misspelled Mertin's water monitor, is a species of lizard in the family Varanidae. The species is endemic to northern Australia, and is a wide-ranging, actively foraging, opportunistic predator of aquatic and riparian habitats.
Mertensia paniculata, also known as the tall lungwort, tall bluebells, or northern bluebells, is an herb or dwarf shrub with drooping bright-blue, bell-shaped flowers. It is native to northwestern North America and the Great Lakes.
Mertensia ovum, also known as the Arctic comb jelly or sea nut, is a cydippid comb jelly or ctenophore first described as Beroe ovum by Johan Christian Fabricius in 1780. Unusually among ctenophores, which normally prefer warmer waters, it is found in the Arctic and adjacent polar seas, mostly in surface waters down to 50 metres .In addition to being weakly bioluminescent in blues and greens, comb jellies produce a rainbow effect similar to that seen on an oil slick, and which is caused by interference of incident light on the eight rows of moving cilia or comb rows which propel the organism.
Mertens stability is a solution concept used to predict the outcome of a non-cooperative game. A tentative definition of stability was proposed by Elon Kohlberg and Jean-François Mertens for games with finite numbers of players and strategies.