Abstract
The Geometry of Numbers is concerned with a study of the relationships between point lattices and sets of points. In this course of lectures I want to give an account of some of the basic general results of the subject. I will confine my attention to the study of what may be called homogeneous problems, and will say nothing about non-homogeneous problems; partly because eight lectures are not too many to devote to the homogeneous problems, and partly because it is the theorems on the homogeneous problems which form the basis of the subject. The results on non-homogeneous problems tend to be rather special or rather simple.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Reference
H.F.BLICHFELDT, Trans.Amer.Math.Soc. , 40 (1914), 227–256.
P.MULLENDER, Proc.Nederl.Akad.v.Wet.,52 (1949) ,50–60.
O.PERRON, Math. Annalen, 83 (1921), 77–84.
H.DAVENP0RT, Quart,J.of Math. 10 (1939), 118–121.
T.ESTERMANN, Journ.London Math. Soc. 21 (1946), 179–182.
C.CHAUBAUTY, Comptes Rendue, 228 (1949), 796–797.
C.A,ROGERS, Proc. K. Ned. Akad. v.Wet. 52 (1949)n 256–263.
V.JARNIK , Vestnik Kralovske Ceske Spolecnosti Nauk (Praha,1941)
K. MAHLER. Proc.K;Ned.Akad.v. Wet. ,52 (1949) ,633–642.
K.MAHLER, Proc. Royal Soc. A, 187 (1946), 151–187 and Proc. K. Ned. .Akad. v,Wet. 49 (1946), 331–343, 444–454, 524–532, 624–631.
H.P.P.SWINNERTON-DYER, Proc. Cambridge Phil.Soc. 49 (1953), 161–162, Our proof follows his closely.
K REINHARDT, Abh. Math.Sem. Hamburg, 10 (1934), 216–230, see also K.Mahler, Proc. K,Ned.Akad.v.Wet. 50 (1947), 692–703.
Nachr. Ges Wiss.Göttingen 1904, 311–355.
JV WHITWORTH,Proc.London Math.Soc. (2),53 (1952),422–442, and Annali di Mat. (4) 27(1948), 29–37.
KH W0LFF, Monaths.Math 58 (1954), 38–56.
JG van dor CORPUT and H.DAVENPORT, Proc. K.Nod.Akad.v. Wet. 49 (1946), 701–707.
A MARKOFF. Math. Annalen 15 (1879), 381–406 and 17 (1880) 379–399. See J.W.S.CASSELS, Annals of Math., 50 (1949) ,676–685.
MORDELL-For a brief account of the history of the. results discus sed in this section see H.DAVENPORT, Proc. International Congress of Mathematicians ,1950, Vol.1, 166–174.
Recently announced in the Bull. Amer. Math, Soc.
ROGERS– Phil. Trans. Royal Soc.A, 242 (1950), 311–344.
Phil. Trans. Royal Soc.,A, 248 (1055), 73–96.
See Journ. London, Math. Soc.26 (1951), 307–310.
E HLAWKA, Math. Zeit, 49 (1944), 285–312.
JWS CASSELS, Proc. Cambridge Philos. Soc. 49 (1953), 165–166, This proof is similar to unpublished proofs found independently by H.Weyl and C.A.Rogers,
Submitted for publication in the Proc. London Math. Soc.
Editor information
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Rogers, C.A. (2011). The Geometry Of Numbers. In: Ricci, G. (eds) Teoria dei numeri. C.I.M.E. Summer Schools, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10892-1_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-10892-1_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10891-4
Online ISBN: 978-3-642-10892-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)