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Sums of squares in quaternion rings

Anna Cooke, Spencer Hamblen, Sam Whitfield
2017 Involve. A Journal of Mathematics  
We determine the minimum necessary number of squares for infinitely many Quaternion rings, and give global upper and lower bounds.  ...  We investigate the analogous question over Quaternion rings, focusing on squares of elements of Quaternion rings with integer coefficients.  ...  We will examine a generalization of Waring's Problem to Quaternion rings. Definition 1.2.  ... 
doi:10.2140/involve.2017.10.651 fatcat:ykbcuuv6jvh3pdzmnq323rj7xe

Book Review: Diophantische Gleichungen

H. S. Vandiver
1942 Bulletin of the American Mathematical Society  
Also, the application of quaternions and related linear algebras to such questions as developed by A. Hurwitz, Dickson and others is not taken up.  ...  where a is a rational integer, and treats by the use of units in K the problem of finding other sets of solutions of (2), having given one set, as well as methods for determining if there exists any set  ... 
doi:10.1090/s0002-9904-1942-07604-x fatcat:q7blvtzjvnbqpghiekcznk7spy

General index 1925-1934—Authors

1936 Bulletin of the American Mathematical Society  
A necessary and sufficient condition for the non-equivalence of any two rational generalized quaternion division algebras, 36, 535.  ...  Integral domains of rational generalized quaternion algebras, 40, 164. Criteria for the solution of a certain quadratic diophantine equation, 37, 608. Ayres, W. L.  ...  Waring 1 s problem for ninth powers, 40, 487. The converse of Waring's problem, 40, 711. See Reviews, under Bell, Fricke. Dines, L. L. Linear inequalities in general analysis, 33, 695.  ... 
doi:10.1090/s0002-9904-1936-06339-1 fatcat:xbyfsg5y4vgknkuk4cremhxp4e

Abstracts of papers

1935 Bulletin of the American Mathematical Society  
In both cases these strips find application in the problem of determining manifolds for which Cauchy's problem is indeterminate.  ...  Titt: (n -1)-dimensional characteristic strips and Cauchy's problem for partial differential equations.  ...  Zuckerman: New results for the number g(n) in Waring's problem. Preliminary report.  ... 
doi:10.1090/s0002-9904-1935-06073-2 fatcat:qdrv3cf5t5ednpoi7sus6ed6ku

The thirty-first annual meeting of the Society

R. G. D. Richardson
1925 Bulletin of the American Mathematical Society  
Hurwitz: Characteristic parameter values for an integral equation.  ...  Hurwitz: A trivial Tauberian theorem.  ... 
doi:10.1090/s0002-9904-1925-04035-5 fatcat:ib37i3dbojdmzip5w22l6576mm

Page 1280 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
, but in this section Additive number theory; partitions Waring’s problem and variants, sums of different powers Additive questions concerning r-free numbers Lattice points in specified regions Goldbach-type  ...  Partitions: multipartite, and related problems Partitions: restricted by congruence, inequality or repetition conditions Partitions: asymptotic, convergent series expansions Partitions: congruences for  ... 

Page 1212 of Mathematical Reviews Vol. 16, Issue Index [page]

Mathematical Reviews  
, but in this section Additive number theory; partitions Waring’s problem and variants, sums of different powers Additive questions concerning r-free numbers Lattice points in specified regions Goldbach-type  ...  Partitions: multipartite, and related problems Partitions: restricted by congruence, inequality or repetition conditions Partitions: asymptotic, convergent series expansions Partitions: congruences for  ... 

Page 1202 of Mathematical Reviews Vol. 17, Issue Index [page]

Mathematical Reviews  
, but in this section Additive number theory; partitions Waring’s problem and variants, sums of different powers Additive questions concerning r-free numbers Lattice points in specified regions Goldbach-type  ...  Partitions: multipartite, and related problems Partitions: restricted by congruence, inequality or repetition conditions Partitions: asymptotic, convergent series expansions Partitions: congruences for  ... 

Page 1849 of Mathematical Reviews Vol. 25, Issue Index [page]

Mathematical Reviews  
number theory; partitions Waring’s problem and variants Lattice points in specified regions Goldbach-type theorems; other additive questions involving primes Applications of the Hardy-Littlewood method  ...  in special residue classes Applications of automorphic functions and forms to multiplicative problems [See also 1 1 Fxx] Generalized primes and integers None of the above, but in this section Additive  ... 

Page 1925 of Mathematical Reviews Vol. 26, Issue Index [page]

Mathematical Reviews  
theory; partitions Waring’s problem and variants Lattice points in specified regions Goldbach-type theorems; other additive questions involving primes Applications of the Hardy-Littlewood method [See  ...  in special residue classes Applications of automorphic functions and forms to multiplicative problems [See also 11Fxx] Generalized primes and integers None of the above, but in this section Additive number  ... 

Page 2391 of Mathematical Reviews Vol. 31, Issue Index [page]

Mathematical Reviews  
theory; partitions Waring’s problem and variants Lattice points in specified regions Goldbach-type theorems; other additive questions involving primes Applications of the Hardy-Littlewood method [See  ...  in special residue classes Applications of automorphic functions and forms to multiplicative problems [See also 11Fxx] Generalized primes and integers None of the above, but in this section Additive number  ... 

Page 2813 of Mathematical Reviews Vol. , Issue Subject Index [page]

Mathematical Reviews  
theory; partitions Waring’s problem and variants Lattice points in specified regions Goldbach-type theorems; other additive questions involving primes Applications of the Hardy-Littlewood method [See  ...  in special residue classes Applications of automorphic functions and forms to multiplicative problems [See also 11Fxx] Generalized primes and integers None of the above, but in this section Additive number  ... 

Page 1787 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
number theory; partitions Waring’s problem and variants Lattice points in specified regions Goldbach-type theorems; other additive questions involving primes Applications of the Hardy-Littlewood method  ...  in special residue classes Applications of automorphic functions and forms to multiplicative problems [See also 11 Fxx] Generalized primes and integers None of the above, but in this section Additive  ... 

Page 1881 of Mathematical Reviews Vol. 24, Issue Index [page]

Mathematical Reviews  
theory; partitions Waring’s problem and variants Lattice points in specified regions Goldbach-type theorems; other additive questions involving primes Applications of the Hardy-Littlewood method [See  ...  in special residue classes Applications of automorphic functions and forms to multiplicative problems [See also 11Fxx] Generalized primes and integers None of the above, but in this section Additive number  ... 

Page 240 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
(with Oh, Byeong-Kweon) Bounds for quadratic Waring’s problem. 2003e:11041  ...  (with Oh, Byeong-Kweon) Bounds for quadratic Waring’s problem. 2003e:11041 Oh, Byeong-Kweon see Kim, Myung-Hwan!, 2003e:11041 Shimura, Goro The representation of integers as sums of squares.  ... 
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