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List of Paul Erd˝Os's Publications in Number Theory

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List of Paul Erd˝Os's Publications in Number Theory ACTA ARITHMETICA LXXXI.4 (1997) List of Paul Erd˝os’spublications in number theory (The name(s) of the coauthor(s) are given at the end of each item.) 1932 32.01 Beweis eines Satzes von Tschebyschef , Acta Litt. Sci. Regiae Univ. Hungar. Fr.-Jos. Sect. Sci. Math. 5 (1932), 194–198. 32.02 Egy K¨ursch´ak-f´eleelemi sz´amelm´eletit´etel´altal´anos´ıt´asa (Generalization of a number- theoretic theorem of K¨ursch´ak,in Hungarian, German summary), Mat. Fiz. Lapok 39 (1932), 17–24. 1934 34.01 A theorem of Sylvester and Schur, J. London Math. Soc. 9 (1934), 282–288. 34.02 Bizonyos sz´amtanisorok t¨orzssz´amair´ol, B¨olcs´eszdoktori´ertekez´es (On primes in some arithmetic progressions, in Hungarian), S´arospatak,1934. 34.03 On a problem in the elementary theory of numbers, Amer. Math. Monthly 41 (1934), 608–611 (P. Tur´an). 34.04 On the density of the abundant numbers, J. London Math. Soc. 9 (1934), 278–282. 34.05 Uber¨ die Anzahl der Abelschen Gruppen gegebener Ordnung und ¨uber ein verwandtes zahlentheoretisches Problem, Acta Litt. Sci. Regiae Univ. Hungar. Fr.-Jos. Sect. Sci. Math. 7 (1934), 95–102 (G. Szekeres). 1935 35.01 Ein zahlentheoretischer Satz, Bull. Inst. Math. M´ec.Univ. Kouybycheff Tomsk 1 (1935), 101–103 (P. Tur´an). 35.02 Note on consecutive abundant numbers, J. London Math. Soc. 10 (1935), 128–131. 35.03 Note on sequences of integers no one of which is divisible by any other, J. London Math. Soc. 10 (1935), 126–128. 35.04 On primitive abundant numbers, J. London Math. Soc. 10 (1935), 49–58. 35.05 On the density of some sequences of numbers, J. London Math. Soc. 10 (1935), 120–125. 35.06 On the difference of consecutive primes, Quart. J. Math. Oxford Ser. 6 (1935), 124–128. 35.07 On the normal number of prime factors of p − 1 and some related problems concerning Euler’s ϕ-function, Quart. J. Math. Oxford Ser. 6 (1935), 205–213. 35.08 The representation of an integer as the sum of the square of a prime and of a square-free integer, J. London Math. Soc. 10 (1935), 243–245. 35.09 Uber¨ die Primzahlen gewisser arithmetischer Reihen, Math. Z. 39 (1935), 473–491. 35.10 Uber¨ die Vereinfachung eines Landauschen Satzes, Bull. Inst. Math. M´ec.Univ. Kouy- bycheff Tomsk 1 (1935), 144–147. [319] 320 List of Paul Erd˝os’spublications 1936 36.01 A generalization of a theorem of Besicovitch, J. London Math. Soc. 11 (1936), 92–98. 36.02 Note on some additive properties of integers, in: Publ. de Congr`esInternat. Math., Oslo, 1936, 1–2. 36.03 On a problem of Chowla and some related problems, Proc. Cambridge Philos. Soc. 32 (1936), 530–540. 36.04 On sequences of positive integers, Acta Arith. 2 (1936), 147–151 (H. Davenport). 36.05 On some sequences of integers, J. London Math. Soc. 11 (1936), 261–264 (P. Tur´an). 36.06 On the arithmetical density of the sum of two sequences one of which forms a basis for the integers, Acta Arith. 1 (1936), 197–200. 36.07 On the integers which are the totient of a product of three primes, Quart. J. Math. Oxford Ser. 7 (1936), 16–19. 36.08 On the integers which are the totient of a product of two primes, Quart. J. Math. Oxford Ser. 7 (1936), 227–229. 36.09 On the representation of an integer as the sum of k k-th powers, J. London Math. Soc. 11 (1936), 133–136. 1937 37.01 Eine Bemerkung ¨uber lineare Kongruenzen, Acta Arith. 2 (1937), 214–220 (V. Jarn´ık). 37.02 Note on the number of prime divisors of integers, J. London Math. Soc. 12 (1937), 308– 314. 37.03 On the density of some sequences of numbers, II , J. London Math. Soc. 12 (1937), 7–11. 37.04 On the easier Waring problem for powers of primes, I , Proc. Cambridge Philos. Soc. 33 (1937), 6–12. 37.05 On the sum and difference of squares of primes, J. London Math. Soc. 12 (1937), 168–171. 37.06 Uber¨ diophantische Gleichungen der Form n! = xp ± yp und n! ± m! = xp, Acta Litt. Sci. Regiae Univ. Hungar. Fr.-Jos. Sect. Sci. Math. 8 (1937), 241–255 (R. Obl´ath). 1938 38.01 Note on the Euclidean algorithm, J. London Math. Soc. 13 (1938), 3–8 (Chao Ko). 38.02 On additive properties of squares of primes, I , Nederl. Akad. Wetensch. Proc. 41 (1938), 3–7. 38.03 On sequences of integers no one of which divides the product of two others and on some related problems, Izv. Nauchn.-Issled. Inst. Mat. i Mekh. Tomsk 2 (1938), 74–82. 38.04 On the asymptotic density of the sum of two sequences one of which forms a basis for the integers, II , Trav. Inst. Math. Tbilissi 3 (1938), 217–224. 38.05 On the density of some sequences of numbers, III , J. London Math. Soc. 13 (1938), 119–127. 38.06 On the number of integers which can be represented by a binary form, J. London Math. Soc. 13 (1938), 134–139 (K. Mahler). 38.07 Some results on definite quadratic forms, J. London Math. Soc. 13 (1938), 217–224 (Chao Ko). P ¨ 1 38.08 Uber die Reihe p , Mathematica B 7 (1938), 1–2. 1939 39.01 Additive arithmetical functions and statistical independence, Amer. J. Math. 61 (1939), 713–721 (A. Wintner). 39.02 An extremum-problem concerning trigonometric polynomials, Acta Litt. Sci. Regiae Univ. Hungar. Fr.-Jos. Sect. Sci. Math. 9 (1939), 113–115. 39.03 Note on products of consecutive integers, J. London Math. Soc. 14 (1939), 194–198. 39.04 Note on the product of consecutive integers, II , J. London Math. Soc. 14 (1939), 245–249. 39.05 On a family of symmetric Bernoulli convolutions, Amer. J. Math. 61 (1939), 974–976. List of Paul Erd˝os’spublications 321 39.06 On definite quadratic forms which are not the sum of two definite or semi-definite forms, Acta Arith. 3 (1939), 102–121 (Chao Ko). 39.07 On sums of positive integral k-th powers, Ann. of Math. 40 (1939), 533–536 (H. Daven- port). 39.08 On the easier Waring problem for powers of primes, II , Proc. Cambridge Philos. Soc. 35 (1939), 149–165. 39.09 On the Gaussian law of errors in the theory of additive functions, Proc. Nat. Acad. Sci. U.S.A. 25 (1939), 206–207 (M. Kac). 39.10 On the integers of the form xk + yk, J. London Math. Soc. 14 (1939), 250–254. 39.11 On the smoothness of the asymptotic distribution of additive arithmetical functions, Amer. J. Math. 61 (1939), 722–725. 39.12 Some arithmetical properties of the convergents of a continued fraction, J. London Math. Soc. 14 (1939), 12–18 (K. Mahler). 1940 40.01 Additive functions and almost periodicity (B2), Amer. J. Math. 62 (1940), 635–645 (A. Wintner). 40.02 On the smoothness properties of a family of Bernoulli convolutions, Amer. J. Math. 62 (1940), 180–186. 40.03 Ramanujan sums and almost periodic functions, Studia Math. 9 (1940), 43–53 (M. Kac; E. R. van Kempen; A. Wintner). 40.04 The difference of consecutive primes, Duke Math. J. 6 (1940), 438–441. 40.05 The dimension of the rational points in Hilbert space, Ann. of Math. 41 (1940), 734–736. 40.06 The Gaussian law of errors in the theory of additive number theoretic functions, Amer. J. Math. 62 (1940), 738–742 (M. Kac). 1941 41.01 On a problem of Sidon in additive number theory, and on some related problems, J. London Math. Soc. 16 (1941), 212–215 (P. Tur´an). 41.02 On some asymptotic formulas in the theory of the “factorisatio numerorum”, Ann. of Math. 42 (1941), 989–993. 41.03 The distribution of the number of summands in the partitions of a positive integer, Duke Math. J. 8 (1941), 335–345 (I. Lehner). 1942 42.01 On an elementary proof of some asymptotic formulas in the theory of partitions, Ann. of Math. 43 (1942), 437–450. 42.02 On the asymptotic density of the sum of two sequences, Ann. of Math. 43 (1942), 65–68. 42.03 On the law of the iterated logarithm, Ann. of Math. 43 (1942), 419–436. 1943 43.01 A note on Farey series, Quart. J. Math. Oxford Ser. 14 (1943), 82–85. 43.02 Corrections to two of my papers, Ann. of Math. 44 (1943), 647–651. 1944 44.01 A conjecture in elementary number theory, Bull. Amer. Math. Soc. 50 (1944), 881–882 (L. Alaoglu). 44.02 On a problem of Sidon in additive number theory and on some related problems. Adden- dum, J. London Math. Soc. 19 (1944), 208. 44.03 On highly composite and similar numbers, Trans. Amer. Math. Soc. 56 (1944), 448–469 (L. Alaoglu). 44.04 On highly composite numbers, J. London Math. Soc. 19 (1944), 130–133. 322 List of Paul Erd˝os’spublications 1945 45.01 Integral distances, Bull. Amer. Math. Soc. 51 (1945), 598–600 (W. H. Anning). 45.02 Integral distances, Bull. Amer. Math. Soc. 51 (1945), 996. 45.03 On certain variations of the harmonic series, Bull. Amer. Math. Soc. 51 (1945), 433–436 (I. Niven). 45.04 On the least primitive root of a prime p, Bull. Amer. Math. Soc. 51 (1945), 131–132. 45.05 Some remarks on Euler’s φ function and some related problems, Bull. Amer. Math. Soc. 51 (1945), 540–544.
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