A Complete Bibliography of the Journal of Number Theory (1960–1969)

Nelson H. F. Beebe University of Utah Department of Mathematics, 110 LCB 155 S 1400 E RM 233 Salt Lake City, UT 84112-0090 USA

Tel: +1 801 581 5254 FAX: +1 801 581 4148

       E-mail: beebe@math.utah.edu, beebe@acm.org,
                  beebe@computer.org (Internet)
      WWW URL: http://www.math.utah.edu/~beebe/

16 July 2020 Version 1.00

Title word cross-reference

−1 [24]. ax^{2} + by^{2} + cz^{2} = 0 [3]. modp [13]. e [32]. k [41]. L [8]. n [41]. P (\sqrt{−2p}) [27]. p = ef + 1 [32]. p ne2 [27].

-functions [8]. -Funktionen [8]. -th [41].

abelian [4, 5, 22]. additive [42]. algebra [20]. algebraic [9, 18, 34, 36]. algebraische [36]. allied [15]. ambiguous [6]. approximable [17]. approximations [21]. April [16]. arguments [8]. Argumentstellen [8]. Asymmetric [35]. asymptotic [21]. auflösbar [36]. Author [55]. automorphisms [25].

Badly [17]. basic [21]. beschränkter [36]. Bestimmung [19]. Beurling [23]. bezüglich [40]. binary [53]. biquadratic [12]. Board [2]. bound [12].

Cayley [20]. Characterization [26]. circle [49]. circulants [32]. Class [9, 12, 19, 27, 29]. class-number [29]. classes [8, 50]. classes- [8]. coefficients [47]. cohomology [6]. combinatorial [5, 22]. compatibility [45]. composite [32]. condition [45]. congruence [25, 43]. Consecutive [46]. Corresponding [34, 44]. cubic [21]. curves [11]. Cyclic [19, 34, 44]. cyclotomic [24]. cyclotomy [32].

Davenport [39]. Dedekind [25]. degree [34, 44]. denen [36]. Determination [19]. diophantine [21]. discriminant [50]. Discriminantal [53]. distribution [15, 41]. divisors [53]. domains [25].

Editorial [2]. equation [3, 36]. every [36]. extensions [34, 44].

factoring [13]. factorization [14, 33]. field [21, 24, 27]. fields [4, 9, 12, 34, 36]. finite [5, 22]. forms [17, 35, 50, 53, 54]. function [43]. functions [8, 15, 29, 42]. Funktionen [8].

Galois [6]. gap [7]. Gauss [12]. Gaussian [46]. genera [4]. generalized [23]. German [8, 19, 27, 36, 40, 43]. Gleichung [36]. groups [5, 10, 22, 25].

Halberstam [39]. Hecke [28]. Heegner [7]. Hensel [33]. homogeneous [35].

ideals [6]. II [22]. index [55]. inequality [35]. Infinite [36]. integer [3, 47]. integers [18, 31, 46]. integral [42]. integral-valued [42]. invariants [37]. isomorphic [49].

January [1]. jede [36]. July [30].

Klassenzahl [27]. Klassenzahlen [19]. Kongruenzeigenschaften [43]. Körpers [27].

lattice [54]. lattice-point [54]. law [48]. Leopoldt [4]. level [36]. limited [36]. linear [10, 17, 25]. Lubin [48].

magnitude [3]. matrices [26]. Mixed [32]. modular [29]. module [45]. Modules [20]. moduli [11]. modulo [32, 41]. Moments [50].

natural [8]. natürlichen [8]. negative [50]. noetherian [10]. non [35, 41, 46]. non-homogeneous [35]. non-residues [41, 46]. norm [54]. Normalität [40]. Normality [40]. note [9, 18]. number [4, 9, 21, 23, 27, 29, 34, 36, 40, 50]. Numbers [8, 9, 19, 23]. Numerical [19]. Numerische [19].

October [38].

Pages [1, 16, 30, 38]. pairs [31]. paper [51, 52]. partition [43]. partitionenfunktion [43]. plane [49]. point [54]. polynomials [14, 47]. positive [31]. power [32, 41, 44]. previous [52]. prime [23, 27, 32, 34, 44]. prime-power [32]. primitive [50]. Primzahl [27]. problem [5, 22, 29, 37, 54]. properties [43]. punctured [49].

quadratic [8, 35, 50, 53]. quadratischer [8]. quartics [13].

rational [37]. Real [8, 19, 21]. reciprocity [48]. reell [8]. reell-quadratischer [8]. reeller [19]. regarding [40]. Remarks [51, 52]. representation [24]. residue [34, 44]. residues [41, 46]. result [39]. Riemann [15]. ring [8]. Ringklassen [8]. Ringklassen- [8]. rings [20]. role [29]. roots [15].

schemes [11]. Schwarz [51]. sets [31]. several [54]. Simultaneous [21]. singularities [11]. solutions [3]. solvable [36]. some [31]. squares [24]. Stufe [36]. submodules [45]. sum [24]. supplement [4]. systems [17, 34, 44].

Tate [48]. ternary [35]. th [41]. theorem [7, 23, 28]. theoretical [40]. theory [4]. transformationen [40]. transformations [40].

Unendliche [36]. unipotent [26]. unit [49].

valued [42]. values [8]. variables [54].

W. [51]. Werte [8]. which [36].

zahlentheoretischer [40]. Zahlkörper [8, 19, 36]. zeta [15]. zyklischer [19].

References

Anonymous:1969:PJa

[1] Anonymous. Pages 1–137 (January 1969). Journal of Number Theory, 1(1): ??, January 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic).

Anonymous:1969:EB

[2] Anonymous. Editorial Board. Journal of Number Theory, 1(1):i, January 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (elec-

tronic). URL http://www.sciencedirect.com/science/article/pii/
0022314X69900183.

Mordell:1969:MIS

[3] L. J. Mordell. On the magnitude of the integer solutions of the equation ax^{2} + by^{2} + cz^{2} = 0. Journal of Number Theory, 1(1):1–3, January 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (elec-

tronic). URL http://www.sciencedirect.com/science/article/pii/
0022314X69900195.

Hasse:1969:SLT

[4] Helmut Hasse. A supplement to Leopoldt’s theory of genera in abelian number fields. Journal of Number Theory, 1(1):4–7, January 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://

www.sciencedirect.com/science/article/pii/0022314X69900201.

Olson:1969:CPFa

[5] John E. Olson. A combinatorial problem on finite Abelian groups, I. Journal of Number Theory, 1(1):8–10, January 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://www.

sciencedirect.com/science/article/pii/0022314X69900213.

Ullom:1969:GCA

[6] S. Ullom. Galois cohomology of ambiguous ideals. Journal of Number Theory, 1(1):11–15, January 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://www.sciencedirect.com/

science/article/pii/0022314X69900225.

Stark:1969:GTH

[7] H. M. Stark. On the “gap” in a theorem of Heegner. Journal of Number Theory, 1(1):16–27, January 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://www.sciencedirect.com/

science/article/pii/0022314X69900237.

Barner:1969:WRF

[8] Klaus Barner. Über die Werte der Ringklassen-L-Funktionen reellquadratischer Zahlkörper an natürlichen Argumentstellen. (German) [On the values of the ring classes-L-functions of real quadratic numbers at natural arguments]. Journal of Number Theory, 1(1):28–64, January 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (elec-

tronic). URL http://www.sciencedirect.com/science/article/pii/
0022314X69900249.

Ishida:1969:NCN

[9] Makoto Ishida. A note on class numbers of algebraic number fields. Journal of Number Theory, 1(1):65–69, January 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://www.

sciencedirect.com/science/article/pii/0022314X69900250.

Zassenhaus:1969:LNG

[10] Hans Zassenhaus. On linear noetherian groups. Journal of Number Theory, 1(1):70–89, January 1969. CODEN JNUTA9. ISSN 0022-314X (print),

1096-1658 (electronic). URL http://www.sciencedirect.com/science/
article/pii/0022314X69900262.

Popp:1969:SMS

[11] Herbert Popp. The singularities of the moduli schemes of curves. Journal of Number Theory, 1(1):90–107, January 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://www.sciencedirect.

com/science/article/pii/0022314X69900274.

Lakein:1969:GBC

[12] R. B. Lakein. A Gauss bound for a class of biquadratic fields. Journal of Number Theory, 1(1):108–112, January 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://www.

sciencedirect.com/science/article/pii/0022314X69900286.

Leonard:1969:FQ

[13] Philip A. Leonard. On factoring quartics (modp). Journal of Number Theory, 1(1):113–115, January 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://www.sciencedirect.com/

science/article/pii/0022314X69900298.

Kempfert:1969:FP

[14] H. Kempfert. On the factorization of polynomials. Journal of Number Theory, 1(1):116–120, January 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://www.sciencedirect.com/

science/article/pii/0022314X69900304.

Halasz:1969:DRR

[15] G. Halász and P. Turán. On the distribution of roots of Riemann zeta and allied functions, I. Journal of Number Theory, 1(1):121–137, January 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (elec-

tronic). URL http://www.sciencedirect.com/science/article/pii/
0022314X69900316.

Anonymous:1969:PA

[16] Anonymous. Pages 139–260 (April 1969). Journal of Number Theory, 1 (2):??, April 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic).

Schmidt:1969:BAS

[17] Wolfgang M. Schmidt. Badly approximable systems of linear forms. Journal of Number Theory, 1(2):139–154, April 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://www.

sciencedirect.com/science/article/pii/0022314X69900328.

Blanksby:1969:NAI

[18] P. E. Blanksby. A note on algebraic integers. Journal of Number Theory, 1(2):155–160, April 1969. CODEN JNUTA9. ISSN 0022-314X (print),

1096-1658 (electronic). URL http://www.sciencedirect.com/science/
article/pii/0022314X6990033X.

Bauer:1969:NBK

[19] Helmut Bauer. Numerische Bestimmung von Klassenzahlen reeller zyklischer Zahlkörper. (German) [Numerical determination of class numbers of real cyclic numbers]. Journal of Number Theory, 1(2):161–162, April 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (elec-

tronic). URL http://www.sciencedirect.com/science/article/pii/
0022314X69900341.

Estes:1969:MRC

[20] Dennis Estes and Gordon Pall. Modules and rings in the Cayley algebra. Journal of Number Theory, 1(2):163–178, April 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://

www.sciencedirect.com/science/article/pii/0022314X69900353.

Adams:1969:SAD

[21] William W. Adams. Simultaneous asymptotic diophantine approximations to a basic of a real cubic number field. Journal of Number Theory, 1(2):179– 194, April 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658

(electronic). URL http://www.sciencedirect.com/science/article/
pii/0022314X69900365.

Olson:1969:CPFb

[22] John E. Olson. A combinatorial problem on finite Abelian groups, II. Journal of Number Theory, 1(2):195–199, April 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http:

//www.sciencedirect.com/science/article/pii/0022314X69900377.

Diamond:1969:PNT

[23] Harold G. Diamond. The prime number theorem for Beurling’s generalized numbers. Journal of Number Theory, 1(2):200–207, April 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://

www.sciencedirect.com/science/article/pii/0022314X69900389.

Chowla:1969:RSS

[24] Paromita Chowla. On the representation of −1 as a sum of squares in a cyclotomic field. Journal of Number Theory, 1(2):208–210, April 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (elec-

tronic). URL http://www.sciencedirect.com/science/article/pii/
0022314X69900390.

OMeara:1969:ALC

[25] O. T. O’Meara and H. Zassenhaus. The automorphisms of the linear congruence groups over Dedekind domains. Journal of Number Theory, 1(2):211–221, April 1969. CODEN JNUTA9. ISSN 0022-314X (print),

1096-1658 (electronic). URL http://www.sciencedirect.com/science/
article/pii/0022314X69900407.

Zassenhaus:1969:CUM

[26] Hans Zassenhaus. Characterization of unipotent matrices. Journal of Number Theory, 1(2):222–230, April 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://www.sciencedirect.com/

science/article/pii/0022314X69900419.

Hasse:1969:KKP

[27] Helmut Hasse. Über die Klassenzahl des Körpers P (\sqrt{−2p}) mit einer Primzahl p ≠ 2. (German) [On the class number of the field P (\sqrt{−2p}) with a prime number p ne2]. Journal of Number Theory, 1(2):231–234, April 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (elec-

tronic). URL http://www.sciencedirect.com/science/article/pii/
0022314X69900420.

Knapowski:1969:TH

[28] S. Knapowski. On a theorem of Hecke. Journal of Number Theory, 1 (2):235–251, April 1969. CODEN JNUTA9. ISSN 0022-314X (print),

1096-1658 (electronic). URL http://www.sciencedirect.com/science/
article/pii/0022314X69900432.

Stark:1969:RMF

[29] H. M. Stark. The role of modular functions in a class-number problem. Journal of Number Theory, 1(2):252–260, April 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http:

//www.sciencedirect.com/science/article/pii/0022314X69900444.

Anonymous:1969:PJb

[30] Anonymous. Pages 261–384 (July 1969). Journal of Number Theory, 1 (3):??, July 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic).

Delange:1969:SSP

[31] Hubert Delange. On some sets of pairs of positive integers. Journal of Number Theory, 1(3):261–279, July 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://www.sciencedirect.

com/science/article/pii/0022314X69900456.

Storer:1969:MCP

[32] Thomas Storer. Mixed cyclotomy, prime-power circulants, and cyclotomy modulo p = ef + 1 for composite e. Journal of Number Theory, 1(3):280– 290, July 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658

(electronic). URL http://www.sciencedirect.com/science/article/
pii/0022314X69900468.

Zassenhaus:1969:HF

[33] Hans Zassenhaus. On Hensel factorization, I. Journal of Number Theory, 1(3):291–311, July 1969. CODEN JNUTA9. ISSN 0022-314X (print),

1096-1658 (electronic). URL http://www.sciencedirect.com/science/
article/pii/0022314X6990047X.

McCulloh:1969:CRS

[34] L. R. McCulloh and W. T. Stout. Corresponding residue systems in cyclic extensions of prime degree over algebraic number fields. Journal of Number Theory, 1(3):312–325, July 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://www.sciencedirect.com/

science/article/pii/0022314X69900481.

Dumir:1969:AIN

[35] Vishwa Chander Dumir. Asymmetric inequality for non-homogeneous ternary quadratic forms. Journal of Number Theory, 1(3):326–345, July 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (elec-

tronic). URL http://www.sciencedirect.com/science/article/pii/
0022314X69900493.

Geyer:1969:UAZ

[36] Wulf-Dieter Geyer. Unendliche algebraische Zahlkörper, über denen jede Gleichung auflösbar von beschränkter Stufe ist. (German) [Infinite algebraic number fields over which every equation is solvable of limited level]. Journal of Number Theory, 1(3):346–374, July 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://www.sciencedirect.

com/science/article/pii/0022314X6990050X.

Giles:1969:PRI

[37] William B. Giles and Donald L. McQuillan. A problem on rational invariants. Journal of Number Theory, 1(3):375–384, July 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://

www.sciencedirect.com/science/article/pii/0022314X69900511.

Anonymous:1969:PO

[38] Anonymous. Pages 385–557 (October 1969). Journal of Number Theory, 1(4):??, October 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic).

Liu:1969:RDH

[39] Ming-Chit Liu. On a result of Davenport and Halberstam. Journal of Number Theory, 1(4):385–389, October 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://www.sciencedirect.

com/science/article/pii/0022314X69900018.

Schweiger:1969:NBZ

[40] F. Schweiger. Normalität bezüglich zahlentheoretischer transformationen. (German) [Normality regarding number theoretical transformations]. Journal of Number Theory, 1(4):390–397, October 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://www.

sciencedirect.com/science/article/pii/0022314X6990002X.

Norton:1969:DPR

[41] Karl K. Norton. On the distribution of k-th power residues and nonresidues modulo n. Journal of Number Theory, 1(4):398–418, October 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (elec-

tronic). URL http://www.sciencedirect.com/science/article/pii/
0022314X69900031.

Delange:1969:IVA

[42] Hubert Delange. On integral-valued additive functions. Journal of Number Theory, 1(4):419–430, October 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://www.sciencedirect.com/

science/article/pii/0022314X69900043.

Herrmann:1969:KPG

[43] Oskar Herrmann. Kongruenzeigenschaften der partitionenfunktion. (German) [Congruence properties of the partition function]. Journal of Number Theory, 1(4):431–458, October 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://www.sciencedirect.com/

science/article/pii/0022314X69900055.

McCulloh:1969:CEP

[44] Leon R. McCulloh. Cyclic extensions of prime power degree and corresponding residue systems. Journal of Number Theory, 1(4):459–466, October 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (elec-

tronic). URL http://www.sciencedirect.com/science/article/pii/
0022314X69900067.

Zassenhaus:1969:CCS

[45] Hans Zassenhaus. A condition for the compatibility of submodules of a module. Journal of Number Theory, 1(4):467–476, October 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://

www.sciencedirect.com/science/article/pii/0022314X69900079.

Jordan:1969:CRN

[46] James H. Jordan. Consecutive residues or non-residues in the Gaussian integers. Journal of Number Theory, 1(4):477–485, October 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://

www.sciencedirect.com/science/article/pii/0022314X69900080.

Gunji:1969:PIC

[47] Hiroshi Gunji and Donald L. McQuillan. On polynomials with integer coefficients. Journal of Number Theory, 1(4):486–493, October 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://

www.sciencedirect.com/science/article/pii/0022314X69900092.

Shiratani:1969:LTR

[48] Katsumi Shiratani. On the Lubin–Tate reciprocity law. Journal of Number Theory, 1(4):494–499, October 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://www.sciencedirect.com/

science/article/pii/0022314X69900109.

Clay:1969:PPI

[49] James R. Clay. The punctured plane is isomorphic to the unit circle. Journal of Number Theory, 1(4):500–501, October 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://

www.sciencedirect.com/science/article/pii/0022314X69900110.

Wolke:1969:MNC

[50] Dieter Wolke. Moments of the number of classes of primitive quadratic forms with negative discriminant. Journal of Number Theory, 1(4):502– 511, October 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658

(electronic). URL http://www.sciencedirect.com/science/article/
pii/0022314X69900122.

Mahler:1969:RPW

[51] K. Mahler. Remarks on a paper by W. Schwarz. Journal of Number Theory, 1(4):512–521, October 1969. CODEN JNUTA9. ISSN 0022-314X (print),

1096-1658 (electronic). URL http://www.sciencedirect.com/science/
article/pii/0022314X69900134.

Chowla:1969:RPP

[52] Paromita Chowla. Remarks on a previous paper. Journal of Number Theory, 1(4):522–524, October 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://www.sciencedirect.com/

science/article/pii/0022314X69900146.

Pall:1969:DDB

[53] Gordon Pall. Discriminantal divisors of binary quadratic forms. Journal of Number Theory, 1(4):525–533, October 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://www.

sciencedirect.com/science/article/pii/0022314X69900158.

Ramachandra:1969:LPP

[54] K. Ramachandra. A lattice-point problem for norm forms in several variables. Journal of Number Theory, 1(4):534–555, October 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (electronic). URL http://

www.sciencedirect.com/science/article/pii/0022314X6990016X.

Anonymous:1969:AI

[55] Anonymous. Author index. Journal of Number Theory, 1(4):557, October 1969. CODEN JNUTA9. ISSN 0022-314X (print), 1096-1658 (elec-

tronic). URL http://www.sciencedirect.com/science/article/pii/
0022314X69900171.