Theory of arithmetic linear transformations and its application to an elementary proof of Dirichlet's theorem

Koichi YAMAMOTO

doi:10.2969/jmsj/00750424

Koichi YAMAMOTO

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JOURNAL FREE ACCESS

1955 Volume 7 Issue Supplement Pages 424-434

DOI https://doi.org/10.2969/jmsj/00750424

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Published: 1955 Received: November 25, 1955 Available on J-STAGE: August 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: August 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) P. G. Ayoub: On Selberg's lemma for algebraic fields, Canad. Journ. Math., 7 (1955), 138-143.
2) L. E. Dickson: History of the theory of numbers, I, Washington 1919.
3) G. H. Hardy and E. M. Wright : An introduction to the theory of numbers, Oxford 1938.
4) F. Mertens: Über Multiplikation und Nichtverschwinden Dirichletscher Reihen, Journ. für Math., 117 (1897), 169-184.
5) E. Landau: Beiträge zur analytischen Zahlentheorie, Rend. Circ. Mat. Palermo, 26 (1908), 297.
6) E. Landau: Vorlesungen über Zahlentheorie, Berlin 1927.
7) J. Popken: On convolutions in number theory, Indagationes Mathematicae, 17 (1955), 10-15.
8) A. Selberg: An elementary proof of Dirichlet's theorem about primes in an arithmetical progression, Ann. Math., 50 (1949), 297-304.
9) A. Selberg: An elementary proof of the prime-number theorem, Ann. Math., 305-313.
10) H. N. Shapiro: On a theorem of Selberg and generalizations, Ann. Math., 51 (1950), 485-497.

Right : [1] P. G. Ayoub: On Selberg's lemma for algebraic fields, Canad. Journ. Math., 7 (1955), 138-143.
[2] L. E. Dickson: History of the theory of numbers, I, Washington 1919.
[3] G. H. Hardy and E. M. Wright: An introduction to the theory of numbers, Oxford 1938.
[4] F. Mertens: Über Multiplikation und Nichtverschwinden Dirichletscher Reihen, Journ. für Math., 117 (1897), 169-184.
[5] E. Landau: Beiträge zur analytischen Zahlentheorie, Rend. Circ. Mat. Palermo, 26 (1908), 297.
[6] E. Landau: Vorlesungen über Zahlentheorie, Berlin 1927.
[7] J. Popken: On convolutions in number theory, Indagationes Mathematicae, 17 (1955), 10-15.
[8] A. Selberg: An elementary proof of Dirichlet's theorem about primes in an arithmetical progression, Ann. Math., 50 (1949), 297-304.
[9] A. Selberg: An elementary proof of the prime-number theorem, Ann. Math., 50 (1949) 305-313.
[10] H. N. Shapiro: On a theorem of Selberg and generalizations, Ann. Math., 51 (1950), 485-497.

Date of correction: August 29, 2006 Reason for correction: - Correction: PDF FILE Details: -

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