Codes Over Algebraic Integer Rings of Cyclotomic Fields

2004 ◽  
Vol 50 (1) ◽  
pp. 194-200 ◽  
Author(s):  
Y. Fan ◽  
Y. Gao
Keyword(s):  
Algebraic Integer ◽  
Cyclotomic Fields ◽  
Integer Rings

Arithmetic definability by formulas with two quantifiers

1992 ◽  
Vol 57 (1) ◽  
pp. 1-11
Author(s):  
Shih Ping Tung
Keyword(s):  
Algebraic Number ◽  
Necessary Conditions ◽  
Algebraic Integer ◽  
Number Fields ◽  
Universal Quantifier ◽  
Existential Quantifier ◽  
Algebraic Number Fields ◽  
Integer Rings

AbstractWe give necessary conditions for a set to be definable by a formula with a universal quantifier and an existential quantifier over algebraic integer rings or algebraic number fields. From these necessary conditions we obtain some undefinability results. For example, N is not definable by such a formula over Z. This extends a previous result of R. M. Robinson.

Ramanujan Expansion over Algebraic Integer Rings

2021 ◽  
Vol 11 (04) ◽  
pp. 442-453
Author(s):  
旭瑞 刘
Keyword(s):  
Algebraic Integer ◽  
Integer Rings

Sums of three integral squares in cyclotomic fields

2003 ◽  
Vol 68 (1) ◽  
pp. 101-106 ◽  
Author(s):  
Chun-Gang Ji
Keyword(s):  
Positive Integer ◽  
Algebraic Integer ◽  
Cyclotomic Field ◽  
Cyclotomic Fields

Let m be an odd positive integer greater than 2 and f the smallest positive integer such that 2f ≡ 1 (mod m). It is proved that every algebraic integer in the cyclotomic field ℚ(ζm) can be expressed as a sum of three integral squares if and only if f is even.

scholarly journals A sequence of algebraic integer relation numbers which converges to 4

2021 ◽  
Vol 294 ◽  
pp. 107665
Author(s):  
Wonyong Jang ◽  
KyeongRo Kim
Keyword(s):  
Algebraic Integer

scholarly journals A GENERALISED KUMMER'S CONJECTURE

2010 ◽  
Vol 52 (3) ◽  
pp. 453-472 ◽  
Author(s):  
M. J. R. MYERS
Keyword(s):  
Natural Number ◽  
Class Numbers ◽  
Cyclotomic Fields ◽  
Rate Of Growth ◽  
Relative Class ◽  
Almost All

AbstractKummer's conjecture predicts the rate of growth of the relative class numbers of cyclotomic fields of prime conductor. We extend Kummer's conjecture to cyclotomic fields of conductor n, where n is any natural number. We show that the Elliott–Halberstam conjecture implies that this generalised Kummer's conjecture is true for almost all n but is false for infinitely many n.

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