Erdős and Multiplicative Number Theory
Paul Erdős was a prolific writer of letters as well as articles. Along with many other mathematicians in areas such as number theory, combinatorics, and set theory, I was on his “mailing list.“ Paul’s letters arrived several times a year from mathematics centers near and far. They typically began, I hope you are well and things are OK in Samland. I am visiting A right now, and leave next week to preach in B. Let f(n) be a function … . This article reviews some of the topics we discussed: estimates of prime number counts, distribution questions for the Euler φ function, and elementary methods in prime number theory.
KeywordsPrime Number Elementary Proof Arithmetic Function Prime Number Theorem Mathematical Review
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- H. G. Diamond, The distribution of values of Euler’s phi function (in Analytic Number Theory, Proc. Sympos. Pure Math., Vol. XXIV, St. Louis Univ., St. Louis, Mo., 1972), pp. 63–75 Amer. Math. Soc., Providence, R.I., 1973.Google Scholar
- -, Elementary methods in the study of the distribution of prime numbers, Bull. Am. Math. Soc. (N.S.) 7 (1982), 553–589.Google Scholar
- H. G. Diamond and P. Erdős, Arithmetic functions whose values are uniformly distributed in (0,∞) (in Proceedings of the Queen’s Number Theory Conference, 1979), 329–378, Queen’s Papers in Pure and Appl. Math., 54, Queen’s Univ., Kingston, Ont., 1980.Google Scholar
- -, On sharp elementary prime number estimates, L’Enseignement Math. 26 (1980), 313–321.Google Scholar
- H. G. Diamond and D. Rhoads, The modulus of continuity of the distribution function of φ(n)/n (in Topics in Classical Number Theory, Vol. I, II, Budapest, 1981), 335–353, Colloq. Math. Soc. János Bolyai, 34, North-Holland, Amsterdam, 1984.Google Scholar
- P. Erdős, Beweis eines Satzes von Tschebyschef, Acta Litt. Sci. Szeged 5 (1932), 194–198.Google Scholar
- A. Selberg, An elementary proof of the prime number theorem, Ann. of Math. (2) 50 (1949), 305–313.Google Scholar