Mathematician:Franz Mertens

Mathematician

Polish mathematician known for his work in analytic number theory.

Nationality

Polish

History

• Born: 20 March 1840 in Schroda, Posen, Prussia (now Środa Wielkopolska, Poland)
• Died: 5 March 1927 in Vienna, Austria

Theorems and Definitions

• Mertens' First Theorem
• Mertens' Second Theorem
• Mertens' Third Theorem
• Mertens' Convergence Theorem

• Mertens Conjecture

• Mertens Function

• Meissel-Mertens Constant (with Daniel Friedrich Ernst Meissel), also known as:

Kronecker's Constant, for Leopold Kronecker

the Hadamard-de la Vallée-Poussin Constant, for Jacques Salomon Hadamard and Charles de la Vallée Poussin

the Prime Reciprocal Constant

Results named for Franz Mertens can be found here.

Definitions of concepts named for Franz Mertens can be found here.

Publications

• 1865: De functione potentiali duarum ellipsoidium homogenearum
• 1874: Ein Beitrag zur analytischen Zahlentheorie (J. für die Reine und Angew. Math Vol. 78: pp. 46 – 62)

• 1887: Invariante Gebilde ternärer Formen
• 1889: Invariante Gebilde quaternärer Formen
• 1895: Dirichletscher Reihen
• 1897: Über eine zahlentheoretische Funktion
• 1901: Zur linearen Transformation der q-Reihen
• 1902: Beweis der Galois'schen Fundamentalsatzes

Also known as

Also known by the Polish form of his first name: Franciszek

Sources

• John J. O'Connor and Edmund F. Robertson: "Franz Mertens": MacTutor History of Mathematics archive