The mathematical work of Morgan Ward

Author:
D. H. Lehmer

Journal:
Math. Comp. **61** (1993), 307-311

MSC:
Primary 01A70; Secondary 11-03

DOI:
https://doi.org/10.1090/S0025-5718-1993-1182245-3

MathSciNet review:
1182245

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References | Similar Articles | Additional Information

**[1]***A generalization of recurrents*, Bull. Amer. Math. Soc.**33**(1927), 477-492. MR**1561403****[2]***General arithmetic*, Proc. Nat. Acad. Sci. U.S.A.**13**(1927), 748-749.**[3]***Postulates for an abstract arithmetic*, Proc. Nat. Acad. Sci. U.S.A.**14**(1928), 907-911.**[4]***A simplification of certain problems in arithmetical division*, Amer. Math. Monthly**35**(1928), 9-14. MR**1521339****[5]***On certain functional relations*, Amer. Math. Monthly**36**(1929), 426-431. MR**1521822****[6]***Certain expansions involving doubly infinite series*, Ann. of Math. (2)**30**(1929), 578-582.**[7]***A certain class of polynomials*, Ann. of Math. (2)**31**(1930), 43-51. MR**1502917****[8]***A generalization of a familiar theorem concerning prime numbers*, J. London Math. Soc.**5**(1930), 106-107.**[9]***The reversion of a power series*, Rend. Circ. Mat. Palermo**54**(1930), 42-46.**[10]***Postulates for the inverse operations in a group*, Trans. Amer. Math. Soc.**32**(1930), 520-526. MR**1501550****[11]***The characteristic number of a sequence of integers satisfying a linear recursion relation*, Trans. Amer. Math. Soc.**33**(1931), 153-165. MR**1501582****[12]***The algebra of recurring series*, Ann. of Math. (2)**32**(1931), 1-9. MR**1502975****[13]***Some arithmetical properties of sequences satisfying a linear recursion relation*, Ann. of Math. (2)**32**(1931), 734-738. MR**1503026****[14]***The distribution of residues in a sequence satisfying a linear recursion relation*, Trans. Amer. Math. Soc.**33**(1931), 166-190. MR**1501583****[15]***Conditions for the solubility of the diophantine equation*, Trans. Amer. Math. Soc.**33**(1931), 712-718. MR**1501611****[16]***The linear form of numbers represented by a homogeneous polynomial in any number of variables*, Ann. of Math. (2)**33**(1932), 324-326. MR**1503056****[17]***On the behaviour of non-static models of the universe when the cosmological term is omitted*, (with R. C. Tolman), Phys. Rev.**39**(1932), 835-843.**[18]***A type of multiplicative diophantine system*, Amer. J. Math.**55**(1933), 67-76. MR**1506944****[19]***A property of recurring series*, Proc. Nat. Acad. Sci. U.S.A.**19**(1933), 914-916.**[20]***The cancellation law in the theory of congruences to a double modulus*, Trans. Amer. Math. Soc.**35**(1933), 254-260. MR**1501682****[21]***The arithmetical theory of linear recurring series*, Trans. Amer. Math. Soc.**35**(1933), 600-628. MR**1501705****[22]***A certain class of trigonometric integrals*, Amer. Math. Monthly**40**(1933), 340-346. MR**1522833****[23]***The representation of Stirling's numbers and Stirling's polynomials as sums of factorials*, Amer. J. Math.**56**(1934), 87-95. MR**1507004****[24]***On the vanishing of the sum of the**powers of the roots of a cubic equation*, Amer. Math. Monthly**41**(1934), 313-316. MR**1523091****[25]***Note on the period of a mark in a finite field*, Bull. Amer. Math. Soc.**40**(1934), 279-281. MR**1562836****[26]***Note on an arithmetical property of recurring series*, Math. Z.**39**(1934), 211-214.**[27]***An arithmetical property of recurring series of the second order*, Bull. Amer. Math. Soc.**40**(1934), 825-828. MR**1562981****[28]***Note on the iteration of functions of one variable*, Bull. Amer. Math. Soc.**40**(1934), 688-690. MR**1562953****[29]***The numerical evaluation of a class of trigonometric series*, Amer. Math. Monthly**41**(1934), 563-565.**[30]***An enumerative problem in the arithmetic of linear recurring series*, Trans. Amer. Math. Soc.**37**(1935), 435-440. MR**1501795****[31]***A determination of all possible systems of strict implication*, Amer. J. Math.**57**(1935), 261-266. MR**1507068****[32]***Conditions for factorization in a set closed under a single operation*, Ann. of Math. (2)**36**(1935), 36-39.**[33]***On the factorization of polynomials to a prime modulus*, Ann. of Math. (2)**36**(1935), 870-874. MR**1503257****[34]***The diophantine equation*, Trans. Amer. Math. Soc.**38**(1935), 447-457.**[35]***A calculus of sequences*, Amer. J. Math.**58**(1936), 255-266. MR**1507149****[36]***The continuous iteration of real functions*, Bull. Amer. Math. Soc.**42**(1936), 393-396. MR**1563308****[37]***The null divisors of linear recurring series*, Duke Math. J.**2**(1936), 472-476. MR**1545940****[38]***Note on divisibility sequences*, Bull. Amer. Math. Soc.**42**(1936), 843-845. MR**1563448****[39]***Linear divisibility sequences*, Trans. Amer. Math. Soc.**41**(1937), 276-286. MR**1501902****[40]***Arithmetic functions on rings*, Ann. of Math. (2)**38**(1937), 725-732. MR**1503363****[41]***Some arithmetical applications of residuation*, Amer. J. Math.**59**(1937), 921-926. MR**1507292****[42]***Residuation in structures over which a multiplication is defined*, Duke Math. J.**3**(1937), 627-636. MR**1546017****[43]***Arithmetical properties of sequences in rings*, Ann. of Math. (2)**39**(1938), 210-219. MR**1503399****[44]***Residuated lattices*, Proc. Nat. Acad. Sci. U.S.A.**24**(1938), 162-164.**[45]***The law of apparition of primes in a Lucasian sequence*, Trans. Amer. Math. Soc.**44**(1938), 68-86. MR**1501963****[46]***Structure residuation*, Ann. of Math. (2)**39**(1938), 558-568. MR**1503424****[47]***A note on divisibility sequences*, Bull. Amer. Math. Soc.**45**(1939), 334-336. MR**1563977****[48]***Evaluations over residuated structures*(with R. P. Dilworth), Ann. of Math. (2)**40**(1939), 328-338. MR**1503460****[49]***Residuated lattices*(with R. P. Dilworth), Trans. Amer. Math. Soc.**45**(1939), 335-354. MR**1501995****[50]***The algebra of lattice functions*, Duke Math. J.**5**(1939), 357-371. MR**1546130****[51]***Ring homomorphisms which are also lattice homomorphisms*, Amer. J. Math.**61**(1939), 783-787. MR**0000010 (1:2b)****[52]***A characterization of Dedekind structures*, Bull. Amer. Math. Soc.**45**(1939), 448-451. MR**1564002****[53]***Note on the general rational solution of the equation*, Amer. J. Math.**61**(1939), 788-790. MR**0000023 (1:4f)****[54]***The lattice theory of ova*(with R. P. Dilworth), Ann. of Math. (2)**40**(1939), 600-608. MR**0000011 (1:2c)****[55]***A characterization of Boolean algebras*(with Garrett Birkhoff), Ann. of Math. (2)**40**(1939), 609-610. MR**0000009 (1:2a)****[56]***Residuated distributive lattices*, Duke Math. J.**6**(1940), 641-651. MR**0002845 (2:120f)****[57]***The arithmetical properties of modular lattices*, Rev. Ci. Lima**430**(1941), 593-603.**[58]***The closure operators of a lattice*, Ann. of Math. (2)**43**(1942), 191-196. MR**0006144 (3:261e)****[59]***Euler's three biquadrate problem*, Proc. Nat. Acad. Sci. U.S.A.**31**(1945), 125-127. MR**0012104 (6:259e)****[60]***Memoir on elliptic divisibility sequences*, Amer. J. Math.**70**(1948), 31-74. MR**0023275 (9:332j)****[61]***Euler's problem on sums of three fourth powers*, Duke Math. J.**15**(1948), 827-837. MR**0027287 (10:283f)****[62]***The law of repetition of primes in an elliptic divisibility sequence*, Duke Math. J.**15**(1948), 941-946. MR**0027286 (10:283e)****[63]***A generalized integral test for convergence of series*, Amer. Math. Monthly**56**(1949), 170-172. MR**1527199****[64]***Note on a paper by C. E. Dickart, R. P. Dilworth and Morgan Ward*, Bull. Amer. Math. Soc.**55**(1949), 1141. MR**0032579 (11:309g)****[65]***Arithmetical properties of the elliptic polynomials arising from the real multiplication of the Jacobi functions*, Amer. J. Math.**72**(1950), 284-302. MR**0033857 (11:502c)****[66]***Arithmetical properties of polynomials associated with lemniscate elliptic functions*, Proc. Nat. Acad. Sci. U.S.A.**36**(1950), 359-362. MR**0036776 (12:159h)****[67]***A class of soluble diophantine equations*, Proc. Nat. Acad. Sci. U.S.A.**37**(1951), 113-114. MR**0041870 (13:13h)****[68]***Prime divisors of second order recurring series*, Duke Math. J.**21**(1954), 607-614. MR**0064073 (16:221f)****[69]***The maximal prime divisors of linear recurrences*, Canad. J. Math.**6**(1954), 455-462. MR**0066408 (16:569i)****[70]***Cyclotomy and the converse of Fermat's theorem*, Amer. Math. Monthly**61**(1954), 564. MR**0063397 (16:115a)****[71]***The intrinsic divisors of Lehmer numbers*, Ann. of Math. (2)**62**(1955), 230-236. MR**0071446 (17:127i)****[72]***On the number of vanishing terms in an integral cubic recurrence*, Amer. Math. Monthly**62**(1955), 155-160. MR**0067136 (16:675b)****[73]***The law of apparition and repetition of primes in a cubic sequence*, Trans. Amer. Math. Soc.**79**(1955), 72-90. MR**0068579 (16:906d)****[74]***The mappings of the positive integers into themselves which preserve division*, Pacific J. Math.**5**(1955), 1013-1023. MR**0075968 (17:826f)****[75]***Tests for primality based on Sylvester's cyclotomic numbers*, Pacific J. Math.**9**(1959), 1269-1272. MR**0108464 (21:7180)****[76]***The vanishing of the homogeneous product sum of the roots of a cubic*, Duke Math. J.**26**(1959), 553-662. MR**0110669 (22:1544)****[77]***Some diophantine problems connected with linear recurrences*, Report of the Institute in the Theory of Numbers, Univ. Colorado, Boulder, Colorado, 1959, pp. 250-257.**[78]***The vanishing of the homogeneous product sum of three letters*, Duke Math. J.**27**(1960), 619-624. MR**0114790 (22:5609)****[79]***The calculation of the complete elliptic integral of the third kind*, Amer. Math. Monthly**67**(1960), 205-213. MR**0136053 (24:B2092)****[80]***The prime divisors of Fibonacci numbers*, Pacific J. Math.**11**(1961), 379-386. MR**0138586 (25:2029)****[81]***The linear p-adic recurrence of order two*, Illinois J. Math.**6**(1962), 40-52. MR**0138585 (25:2028)****[82]***Divisors of recurrent sequences*(with E. C. Dade, D. W. Robinson, O. Taussky), J. Reine Angew. Math.**214/215**(1964), 180-183. MR**0161875 (28:5079)**

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DOI:
https://doi.org/10.1090/S0025-5718-1993-1182245-3

Article copyright:
© Copyright 1993
American Mathematical Society