Reference Database
(references for the Prime Pages)
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This is the Prime Pages' interface to our BibTeX database.  Rather than being an exhaustive database, it just lists the references we cite on these pages.  Please let me know of any errors you notice.
References: [ Home | Author index | Key index | Search ]

All items with keys beginning with the letter(s): l

D. N. Lehmer, List of primes numbers from 1 to 10,006,721, Carnegie Institution Washington, D.C., 1914.
D. N. Lehmer, Factor table for the first ten millions containing the smallest factor of every number not divisible by 2, 3, 5, or 7 between the limits of 0 and 10017000, Carnegie Institution of Washington, publication 105 1909.  Washington, D.C.,
D. H. Lehmer, "On certain chains of primes," Proc. Lond. Math. Soc., series 3, 14a (1965) 183--186.  MR 31:2222
D. N. Lehmer, "An extended theory of Lucas' functions," Ann. Math., 31 (1930) 419-448.  Reprinted in Selected Papers, D. McCarthy editor, v. 1, Ch. Babbage Res. Center, St. Pierre, Manitoba Canada, pp. 11-48 (1981).
D. H. Lehmer, "Note on Mersenne numbers," Bull. Amer. Math. Soc., 38 (1932) 383-384.
D. H. Lehmer, "On Lucas's test for the primality of Mersenne's numbers," J. London Math. Soc., 10 (1935) 162-165.
D. H. Lehmer, "On the converse of Fermat's theorem," Amer. Math. Monthly, 43 (1936) 347-354.  Errata in Math. Tables Aids Comput. 2 (1947), 279; Math. Comp. 25 (1971) 943.  MR 53:4460
D. H. Lehmer, "A new Mersenne prime," Math. Tables Aids Comput., 6 (1952) 205.
D. H. Lehmer, "Note 131: recent discoveries of large primes," Math. Tables Aids Comput., 6 (1952) 61. (Annotation available)
D. H. Lehmer, "Two new Mersenne primes," Math. Tables Aids Comput., 7 (1953) 72.
R. Lenoble, Mersenne; ou, la naissance du mécanisme, 2nd edition edition, Vrin, 1971.  Paris, First edition 1943..
Lenstra, Jr., H. W., Primality testing algorithms (after Adleman, Rumely and Williams).  In "Bourbaki Seminar, Vol. 1980/81," Lecture Notes in Math. Vol, 901, Springer, Berlin, 1981.  pp. 243--257, MR647500
Lenstra, Jr., H. W., "Miller's primality test," Inform. Process. Lett., 8 (1979) 86-88.  MR 80c:10008
Lenstra, Jr., H. W., Primality testing.  In "Computational Methods in Number Theory, part I," Lenstra, Jr., H. W. and R. Tijdemann editors, Vol, 154, Math. Centre Tract, 1982.  Amsterdam, pp. 55--77, MR 85g:11117 [Introduces Lenstra's Galois theory test]
Lenstra, Jr., H. W., Primality testing.  In "Mathematics and Computer Science: Proceedings of the CWI Symposium," Bakker, J. W. de, M. Hazewinkel and J. K. Lenstra editors, North-Holland, Amsterdam, 1986.  pp. 269-287, MR 88b:11087
Lenstra, Jr., H. W., "Factoring integers with elliptic curves," Ann. Math., 126 (1987) 649-673.  MR 89g:11125
N. Levinson, "More than one third of the zeros of Riemann's zeta-function are on σ =1/2," Adv. Math., 13 (1974) 383--436.  MR 58:27837
K. Lewis, "Smith numbers: an infinite subset of N," Master's thesis, M.S., Eastern Kentucky University, (1994)
E. H. Linfoot, Recent advances in optics, Clarendon Press, 1955.  MR 17,106g
J. E. Littlewood, "Sur la distribution des nombres premiers," C. R. Acad. Sci Paris, 158 (1914) 1869--1872.
Lenstra, Jr., A. K. and Lenstra, Jr., H. W., Algorithms in number theory.  In "Handbook of Theoretical Computer Science, Vol A: Algorithms and Complexity," The MIT Press, 1990.  Amsterdam and New York, pp. 673-715, MR 1 127 178
A. K. Lenstra, Lenstra, Jr., H. W., M. S. Manasse and J. M. Pollard, "The factorization of the ninth Fermat number," Math. Comp., 61 (1993) 319-349.  Addendum, Math. Comp. 64 (1995), 1357.  MR 1 303 085
C. Lalout and J. Meeus, "Nearly-doubled primes," J. Recreational Math., 13 (1980-81) 30--35.
J. C. Lagaris, V. S. Miller and A. M. Odlyzko, "Computing π(x): the Meissel-Lehmer method," Math. Comp., 44 (1985) 537-560.  MR 86h:11111
B. A. LaMacchia and A. M. Odlyzko, "Computation of discrete logarithms in prime fields," Designs, Codes and Cryptography, 1 (1991) 46-62.  MR 92j:11148
G. Löh, "Long chains of nearly doubled primes," Math. Comp., 53 (1989) 751-759.  MR 90e:11015 (Abstract available) [Chains of primes for which each is either twice the proceeding one plus one, or each is either twice the proceeding one minus one. See also [Guy94, section A7].]
W. Looff, "Ueber die Periodicitäte der Decimalbrüche," Archiv der Mathematik und Physics, 16 (1851) 54--57. [Includes the prime 999999000001 in his table with a question mark. However Reuschle [[Reuschle1856], pp. 3, 18] claims Looff had proven it prime.]
M. Lothaire,"Combinatorics on Words" in Encylopedia of mathematics and its applications.  Vol, 17, Addison-Wesley, 1983.  pp. xix+238, ISBN 0-201-13516-7. MR 84g:05002
L. J. Lander and T. R. Parkin, "Consecutive primes in arithmetic progression," Math. Comp., 21 (1967) 489.
Luca, F. and Porubský, S., "The multiplicative group generated by the Lehmer numbers," Fibonacci Quart., 41:2 (2003) 122--132.  MR1990520
L. J. Lander and T. R. Parkin, "On first appearance of prime differences," Math. Comp., 21:99 (1967) 483-488.  MR 37:6237
Lygeros, N. and Rozier, O., "Odd prime values of the ramanujan tau function," Ramanujan J., (2013) 1--12.  available from  (
Leyendekkers, J. V., Rybak, J. M. and Shannon, A. G., "An analysis of Mersenne-Fibonacci and Mersenne-Lucas primes," Notes Number Theory Discrete Math., 5:1 (1999) 1--26.  MR 1738744
J. van de Lune, H. J. J. te Riele and D. T. Winter, "On the zeros of the Riemann zeta function in the critical strip. IV," Math. Comp., 46 (1986) 667-681.  MR 87e:11102 [The first 1,500,000,001 nontrivial zeros of the Riemann zeta function.]
F. Luca, "On a conjecture of erdos and stewart," Math. Comp., 70 (2001) 893--896.  MR 2001g:11042 (Abstract available) [Luca proves that the equation in the abstract has no solutions for n ≥ 6.]
E. Lucas, "Theorie des fonctions numeriques simplement periodiques," Amer. J. Math., 1 (1878) 184--240 and 289--231.
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