This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Adleman, L.M. and Heath-Brown, D.R., The first case of Fermât’s last theorem, Invent. Math., 79 (1985) 409–416.
Bateman, P.T. and Horn, R.A., A heuristic asymptotic formula concern¬ing the distribution of prime numbers, Math. Comp., 16 (1962), 363–367.
Bombieri, E., Friedlander, J.B. and Iwaniec, H., Primes in arithmetic pro¬gressions to large moduli, HI, J. Amer. Math. Soc., 2 (1989) 215–224.
Dickson, L.E., A new extension of Dirichlet’s theorem on prime numbers, Messenger of Math., 33 (1904) 155–161.
Elliott, P.D.T.A. and Halberstam, H., A conjecture in prime number theory, Symp. Math., 4 (1968–9), 59–72.
Granville, A., Least Primes in Arithmetic Progressions, in: J.-M. de Köninck and C. Levesque (eds.), Théorie des nombres (Proceedings of the International Number Theory Conference at Laval, Quebec, 1987), de Gruyter, New York 1989, pp. 306–321.
Granville, A., Some conjectures related to Fermât’s Last Theorem, to appear in the Proceedings of the First Conference of the Canadian Number Theory Association, 1988.
Granville, A., Diophantine Equations with varying exponents, (Ph.D. Thesis, Queen’s University), 1987.
Halberstam, H. and Richert, H.-E., Sieve Methods, (Academic Press), 1974.
Hardy, G.H. and Littlewood, J., Some problems of partitio numerantium III. On the expression of a number as a sum of primes, Acta Math., 44 (1923), 1–70.
Heath-Brown, D.R., Almost primes in arithmetic progressions and short intervals, Math. Proc. Camb. Phil. Soc., 83 (1978) 357–375.
Linnik, U.V., On the least prime in an arithmetic progression II, The Deuring-Heilbronn phenomenon, Ree. Math. [Math. Sb.] N.S. 15(57) (1944) 347–368.
McCurley, K.S., The least r-free number in an arithmetic progression, Trans. Amer. Math. Soc., 293 (1986) 467–475.
Ribenboim, P., 13 Lectures on Fermât’s Last Theorem, (Springer-Verlag, New York) 1979.
Schinzel, A and Sierpinski, W., Sur certaines hypothèses concernant les nombres premiers, Acta Arith. 4 (1958), 185–208; erratum 5 (1959), 259.
Wagstaff, S.S. Jr., Greatest of the least primes in arithmetic progresssions having a given modulus, Math. Comp., 33 (1979) 1073–1080.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Additional information
Dedicated to Paul Bateman on his retirement
Rights and permissions
Copyright information
© 1990 Birkhäuser Boston
About this chapter
Cite this chapter
Granville, A. (1990). Some Conjectures in Analytic Number Theory And their Connection With Fermat’s Last Theorem. In: Berndt, B.C., Diamond, H.G., Halberstam, H., Hildebrand, A. (eds) Analytic Number Theory. Progress in Mathematics, vol 85. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3464-7_19
Download citation
DOI: https://doi.org/10.1007/978-1-4612-3464-7_19
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-3481-0
Online ISBN: 978-1-4612-3464-7
eBook Packages: Springer Book Archive