Davenport, H. [Davenport, James H.] The higher arithmetic. Editing and additional material by James H. Davenport. ICM Edition. Reprint of the 8th edition 2008. (English) Zbl 07661696 Cambridge: Cambridge University Press (ISBN 978-0-521-16989-9/pbk). ix, 239 p. (2023). MSC: 11-01 11A07 11A15 11A41 11Y05 11D04 11Y11 11D09 11Y16 11D25 11H55 11A55 PDF BibTeX XML Cite \textit{H. Davenport}, The higher arithmetic. Editing and additional material by James H. Davenport. ICM Edition. Reprint of the 8th edition 2008. Cambridge: Cambridge University Press (2023; Zbl 07661696)
Vaishya, Lalit; Sharma, Richa A class of fruit Diophantine equations. (English) Zbl 07605285 Monatsh. Math. 199, No. 4, 899-907 (2022). MSC: 11D25 14H52 PDF BibTeX XML Cite \textit{L. Vaishya} and \textit{R. Sharma}, Monatsh. Math. 199, No. 4, 899--907 (2022; Zbl 07605285) Full Text: DOI
Huang, Chao; Pan, Hao A new characterisation for quartic residuacity of 2. (English) Zbl 1500.11004 Bull. Aust. Math. Soc. 106, No. 1, 1-6 (2022). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11A15 05A05 11A07 PDF BibTeX XML Cite \textit{C. Huang} and \textit{H. Pan}, Bull. Aust. Math. Soc. 106, No. 1, 1--6 (2022; Zbl 1500.11004) Full Text: DOI
Das, Shamik; Saikia, Anupam Families of even noncongruent numbers with arbitrarily many pairs of prime factors. (English) Zbl 07555148 Rocky Mt. J. Math. 52, No. 2, 471-481 (2022). MSC: 11G05 11D25 11A15 PDF BibTeX XML Cite \textit{S. Das} and \textit{A. Saikia}, Rocky Mt. J. Math. 52, No. 2, 471--481 (2022; Zbl 07555148) Full Text: DOI Link
Stevenhagen, Peter Redei reciprocity, governing fields and negative Pell. (English) Zbl 1514.11073 Math. Proc. Camb. Philos. Soc. 172, No. 3, 627-654 (2022). Reviewer: Abdelmalek Azizi (Oujda) MSC: 11R11 11R37 11R16 PDF BibTeX XML Cite \textit{P. Stevenhagen}, Math. Proc. Camb. Philos. Soc. 172, No. 3, 627--654 (2022; Zbl 1514.11073) Full Text: DOI arXiv
Nyblom, Michael A closed form for representing integers as sums and differences of cubes. (English) Zbl 1496.11053 J. Integer Seq. 25, No. 4, Article 22.4.4, 9 p. (2022). Reviewer: Arman Shamsi Zargar (Ardabil) MSC: 11D25 11A15 11D85 PDF BibTeX XML Cite \textit{M. Nyblom}, J. Integer Seq. 25, No. 4, Article 22.4.4, 9 p. (2022; Zbl 1496.11053) Full Text: Link
Abate, Marco Book review of: A. Granville, Number theory revealed: an introduction; Number theory revealed: a masterclass. (English) Zbl 1461.00011 Math. Intell. 43, No. 1, 128-129 (2021). MSC: 00A17 11-01 11A05 11A07 11A15 11A41 11A51 11B39 11D04 11D07 11A55 11B30 11D09 11D25 11N05 11N25 PDF BibTeX XML Cite \textit{M. Abate}, Math. Intell. 43, No. 1, 128--129 (2021; Zbl 1461.00011) Full Text: DOI
Sun, Zhi-Wei Quadratic residues and quartic residues modulo primes. (English) Zbl 1471.11013 Int. J. Number Theory 16, No. 8, 1833-1858 (2020). MSC: 11A15 11A07 11B39 PDF BibTeX XML Cite \textit{Z.-W. Sun}, Int. J. Number Theory 16, No. 8, 1833--1858 (2020; Zbl 1471.11013) Full Text: DOI arXiv
Sun, Zhihong Eisenstein and cubic, quartic reciprocity laws. (English) Zbl 1463.01040 J. Nanjing Univ., Math. Biq. 36, No. 2, 185-200 (2019). MSC: 01A70 11-03 11A15 PDF BibTeX XML Cite \textit{Z. Sun}, J. Nanjing Univ., Math. Biq. 36, No. 2, 185--200 (2019; Zbl 1463.01040) Full Text: DOI
Granville, Andrew Number theory revealed: a masterclass. (English) Zbl 1454.11002 Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-4158-6/hbk; 978-1-4704-5424-1/ebook). xxviii, 587 p. (2019). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11-01 11A55 11B30 11B39 11D09 11D25 11N05 11N25 PDF BibTeX XML Cite \textit{A. Granville}, Number theory revealed: a masterclass. Providence, RI: American Mathematical Society (AMS) (2019; Zbl 1454.11002)
Huong, Phạm Lan On the Diophantine equation \(x^3 + y^3 + z^3 = q\). (English) Zbl 1447.11048 Int. J. Number Theory 14, No. 8, 2205-2217 (2018). MSC: 11D25 PDF BibTeX XML Cite \textit{P. L. Huong}, Int. J. Number Theory 14, No. 8, 2205--2217 (2018; Zbl 1447.11048) Full Text: DOI
Aebi, Christian; Cairns, Grant The quartic residues Latin square. (English) Zbl 1412.11004 Integers 17, Paper A35, 6 p. (2017). MSC: 11A15 05B15 PDF BibTeX XML Cite \textit{C. Aebi} and \textit{G. Cairns}, Integers 17, Paper A35, 6 p. (2017; Zbl 1412.11004) Full Text: arXiv Link
Dukkipati, Ambedkar; Palimar, Sushma Primes of the form \(x^2 + d y^2\) with \(x\equiv 0\pmod N\) or \(y\equiv 0\pmod N\). (English) Zbl 1422.11229 Proc. Indian Acad. Sci., Math. Sci. 127, No. 1, 35-43 (2017). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11R37 11R11 11R16 11A41 PDF BibTeX XML Cite \textit{A. Dukkipati} and \textit{S. Palimar}, Proc. Indian Acad. Sci., Math. Sci. 127, No. 1, 35--43 (2017; Zbl 1422.11229) Full Text: DOI arXiv
Sun, Zhi-Hong Quartic residues and sums involving \({4k}\choose{2k}\). (English) Zbl 1357.11006 Taiwanese J. Math. 19, No. 3, 803-818 (2015). MSC: 11A07 11A15 11B39 11B65 11E25 PDF BibTeX XML Cite \textit{Z.-H. Sun}, Taiwanese J. Math. 19, No. 3, 803--818 (2015; Zbl 1357.11006) Full Text: DOI
Shankar, Arul; Wang, Xiaoheng Laws of composition and arithmetic statistics: from Gauss to Bhargava. (English) Zbl 1347.11039 Math. Stud. 84, No. 3-4, 159-171 (2015). MSC: 11E76 11A15 11D25 11D41 11E04 11E08 11E41 PDF BibTeX XML Cite \textit{A. Shankar} and \textit{X. Wang}, Math. Stud. 84, No. 3--4, 159--171 (2015; Zbl 1347.11039)
Evans, Ronald J.; Williams, Kenneth S. Quartic residuacity and the quadratic character of certain quadratic irrationalities. (English) Zbl 1381.11006 Int. J. Number Theory 11, No. 8, 2487-2503 (2015). MSC: 11A15 11E25 PDF BibTeX XML Cite \textit{R. J. Evans} and \textit{K. S. Williams}, Int. J. Number Theory 11, No. 8, 2487--2503 (2015; Zbl 1381.11006) Full Text: DOI
Mezroui, Soufiane; Azizi, Abdelmalek; Ziane, M’hammed Quaternary quartic forms representing infinitely many prime squares. (English) Zbl 1391.11068 Asian-Eur. J. Math. 8, No. 3, Article ID 1550062, 13 p. (2015). Reviewer: M. Rafiq Omar (Bellville) MSC: 11E20 11E76 PDF BibTeX XML Cite \textit{S. Mezroui} et al., Asian-Eur. J. Math. 8, No. 3, Article ID 1550062, 13 p. (2015; Zbl 1391.11068) Full Text: DOI
Sun, Zhi-Hong Congruences for \(q^{[p/8]}\pmod p\) under the condition \(4n^2p = x^2 + qy^2\). (English) Zbl 1390.11012 Int. J. Number Theory 11, No. 4, 1301-1312 (2015). MSC: 11A15 11A07 11E25 PDF BibTeX XML Cite \textit{Z.-H. Sun}, Int. J. Number Theory 11, No. 4, 1301--1312 (2015; Zbl 1390.11012) Full Text: DOI
Sun, Zhi-Hong New reciprocity laws for octic residues and nonresidues. (English) Zbl 1394.11004 J. Number Theory 147, 694-707 (2015). MSC: 11A15 11A07 11B39 11E25 PDF BibTeX XML Cite \textit{Z.-H. Sun}, J. Number Theory 147, 694--707 (2015; Zbl 1394.11004) Full Text: DOI
Halter-Koch, Franz Quadratic irrationals. An introduction to classical number theory. (English) Zbl 1271.11001 Pure and Applied Mathematics (Boca Raton) 306. Boca Raton, FL: CRC Press (ISBN 978-1-4665-9183-7/hbk; 978-1-4665-9184-4/ebook). xvi, 415 p. (2013). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11-01 11R11 11R29 11E16 11A55 11M06 11N05 PDF BibTeX XML Cite \textit{F. Halter-Koch}, Quadratic irrationals. An introduction to classical number theory. Boca Raton, FL: CRC Press (2013; Zbl 1271.11001) Full Text: DOI
Sun, Zhihong On the quartic character of quadratic units. (English) Zbl 1287.11005 Acta Arith. 159, No. 1, 89-100 (2013). MSC: 11A15 11A07 11B39 11E25 PDF BibTeX XML Cite \textit{Z. Sun}, Acta Arith. 159, No. 1, 89--100 (2013; Zbl 1287.11005) Full Text: DOI
Sun, Zhihong Congruences for \(q^{[p/8]}\pmod p\). (English) Zbl 1292.11007 Acta Arith. 159, No. 1, 1-25 (2013). MSC: 11A15 11A07 11E25 PDF BibTeX XML Cite \textit{Z. Sun}, Acta Arith. 159, No. 1, 1--25 (2013; Zbl 1292.11007) Full Text: DOI
Martin, Greg; Pollack, Paul The average least character non-residue and further variations on a theme of Erdős. (English) Zbl 1275.11007 J. Lond. Math. Soc., II. Ser. 87, No. 1, 22-42 (2013). MSC: 11A15 11L40 11R16 PDF BibTeX XML Cite \textit{G. Martin} and \textit{P. Pollack}, J. Lond. Math. Soc., II. Ser. 87, No. 1, 22--42 (2013; Zbl 1275.11007) Full Text: DOI arXiv
Budden, Mark; Calkins, Nicole; Hack, William Nathan; Lambert, Joshua; Thompson, Kimberly Enumeration of triangles in quartic residue graphs. (English) Zbl 1244.11007 Integers 12, No. 1, 57-73 (2012); 11, A48, 17 p. (2011). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11A15 05C38 11T23 11R16 PDF BibTeX XML Cite \textit{M. Budden} et al., Integers 12, No. 1, 57--73 (2012; Zbl 1244.11007) Full Text: DOI EMIS
Sun, Zhihong Congruences for \((A+\sqrt {A^2+mB^2})^{(p-1)/2}\) and \((b+\sqrt{a^2+b^2})^{(p-1)/4}\pmod p\). (English) Zbl 1238.11005 Acta Arith. 149, No. 3, 275-296 (2011). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11A15 11A07 11B39 11E25 PDF BibTeX XML Cite \textit{Z. Sun}, Acta Arith. 149, No. 3, 275--296 (2011; Zbl 1238.11005) Full Text: DOI
Davenport, Harold The higher arithmetic. An introduction to the theory of numbers. Translated from the English by B. Z. Moroz. 2nd edition. (Высшая арифметика. Введение в теорию чисел.) (Russian) Zbl 1390.11001 Fiziko-Matematicheskoe Nasledie. Moscow: Knizhnyĭ Dom “LIBROKOM” (ISBN 978-5-397-01298-0). 175 p. (2010). MSC: 11-01 11A07 11A15 11A41 11Y05 11D04 11Y11 11D09 11Y16 11D25 11H55 11A55 PDF BibTeX XML Cite \textit{H. Davenport}, Высшая арифметика. Введение в теорию чисел (Russian). 2nd edition. Moscow: Knizhnyĭ Dom ``LIBROKOM'' (2010; Zbl 1390.11001)
He, Debiao; Chen, Jianhua; Wang, Yu On Diophantine equation \(3a^2x^4 - By^2 = 1\). (English) Zbl 1231.11033 Ann. Mat. Pura Appl. (4) 189, No. 4, 679-687 (2010). MSC: 11D25 PDF BibTeX XML Cite \textit{D. He} et al., Ann. Mat. Pura Appl. (4) 189, No. 4, 679--687 (2010; Zbl 1231.11033) Full Text: DOI
Sun, Zhihong Quartic, octic residues and Lucas sequences. (English) Zbl 1183.11001 J. Number Theory 129, No. 3, 499-550 (2009). Reviewer: Pieter Moree (Bonn) MSC: 11A15 11A07 11B39 11E25 PDF BibTeX XML Cite \textit{Z. Sun}, J. Number Theory 129, No. 3, 499--550 (2009; Zbl 1183.11001) Full Text: DOI
Davenport, Harold [Davenport, James H.] The higher arithmetic. An introduction to the theory of numbers. Editing and additional material by James H. Davenport. 8th revised ed. (English) Zbl 1204.11002 Cambridge: Cambridge University Press (ISBN 978-0-521-72236-0/pbk). ix, 239 p. (2008). Reviewer: Štefan Porubský (Praha) MSC: 11-01 11A07 11A15 11A41 11Y05 11D04 11Y11 11D09 11Y16 11D25 11H55 11A55 PDF BibTeX XML Cite \textit{H. Davenport}, The higher arithmetic. An introduction to the theory of numbers. Editing and additional material by James H. Davenport. 8th revised ed. Cambridge: Cambridge University Press (2008; Zbl 1204.11002)
Liu, Li; Zhou, Weiping On conjectures concerning class number of binary quadratic forms. (English) Zbl 1266.11005 Sci. Magna 2, No. 2, 7-14 (2006). MSC: 11A15 11E16 11E25 11E41 PDF BibTeX XML Cite \textit{L. Liu} and \textit{W. Zhou}, Sci. Magna 2, No. 2, 7--14 (2006; Zbl 1266.11005)
Sun, Zhihong On the number of incongruent residues of \(x^4+ax^2+bx\) modulo \(p\). (English) Zbl 1205.11009 J. Number Theory 119, No. 2, 210-241 (2006). Reviewer: Pieter Moree (Bonn) MSC: 11A07 11A15 11G20 11L10 PDF BibTeX XML Cite \textit{Z. Sun}, J. Number Theory 119, No. 2, 210--241 (2006; Zbl 1205.11009) Full Text: DOI
Sun, Zhihong Quartic residues and binary quadratic forms. (English) Zbl 1101.11003 J. Number Theory 113, No. 1, 10-52 (2005). Reviewer: Pieter Moree (Bonn) MSC: 11A15 11E25 11B39 PDF BibTeX XML Cite \textit{Z. Sun}, J. Number Theory 113, No. 1, 10--52 (2005; Zbl 1101.11003) Full Text: DOI
Sun, Zhihong Values of Lucas sequences modulo primes. (English) Zbl 1076.11009 Rocky Mt. J. Math. 33, No. 3, 1123-1145 (2003). Reviewer: Franz Lemmermeyer (Bilkent) MSC: 11B39 11A15 11B50 PDF BibTeX XML Cite \textit{Z. Sun}, Rocky Mt. J. Math. 33, No. 3, 1123--1145 (2003; Zbl 1076.11009) Full Text: DOI
Sun, Zhihong Cubic and quartic congruences modulo a prime. (English) Zbl 1033.11003 J. Number Theory 102, No. 1, 41-89 (2003). Reviewer: Pieter Moree (Amsterdam) MSC: 11A07 11B39 11B50 11A15 PDF BibTeX XML Cite \textit{Z. Sun}, J. Number Theory 102, No. 1, 41--89 (2003; Zbl 1033.11003) Full Text: DOI
Cohen, Henri Enumerating quartic dihedral extensions of \(\mathbb Q\) with signatures. (English) Zbl 1114.11085 Ann. Inst. Fourier 53, No. 2, 339-377 (2003). MSC: 11R16 11R29 11R45 11Y40 PDF BibTeX XML Cite \textit{H. Cohen}, Ann. Inst. Fourier 53, No. 2, 339--377 (2003; Zbl 1114.11085) Full Text: DOI Numdam EuDML
Sun, Zhihong Supplements to the theory of quartic residues. (English) Zbl 1049.11007 Acta Arith. 97, No. 4, 361-377 (2001). Reviewer: Franz Lemmermeyer (Bilkent) MSC: 11A15 11E25 PDF BibTeX XML Cite \textit{Z. Sun}, Acta Arith. 97, No. 4, 361--377 (2001; Zbl 1049.11007) Full Text: DOI
Helou, Charles A note on the power residue symbol. (English) Zbl 0972.11103 Jutila, Matti (ed.) et al., Number theory. Proceedings of the Turku symposium on number theory in memory of Kustaa Inkeri, Turku, Finland, May 31-June 4, 1999. Berlin: de Gruyter. 125-129 (2001). Reviewer: Franz Lemmermeyer (San Marcos) MSC: 11R18 11A15 PDF BibTeX XML Cite \textit{C. Helou}, in: Number theory. Proceedings of the Turku symposium on number theory in memory of Kustaa Inkeri, Turku, Finland, May 31--June 4, 1999. Berlin: de Gruyter. 125--129 (2001; Zbl 0972.11103)
Zaharescu, Alexandru A metric symbol for pairs of polynomials over local fields. (English) Zbl 0972.11111 C. R. Math. Acad. Sci., Soc. R. Can. 22, No. 4, 147-150 (2000). Reviewer: Gabriel D.Villa-Salvador (México) MSC: 11S05 11D25 PDF BibTeX XML Cite \textit{A. Zaharescu}, C. R. Math. Acad. Sci., Soc. R. Can. 22, No. 4, 147--150 (2000; Zbl 0972.11111)
Lemmermeyer, Franz Reciprocity laws. From Euler to Eisenstein. (English) Zbl 0949.11002 Springer Monographs in Mathematics. Berlin: Springer. xix, 487 p. (2000). Reviewer: Hans Opolka (Braunschweig) MSC: 11-03 11A15 01-01 11-01 11R18 11R37 PDF BibTeX XML Cite \textit{F. Lemmermeyer}, Reciprocity laws. From Euler to Eisenstein. Berlin: Springer (2000; Zbl 0949.11002)
Davenport, H. The higher arithmetic. An introduction to the theory of numbers. Chapter VIII by J. H. Davenport. 7th ed. (English) Zbl 0958.11002 Cambridge: Cambridge University Press. 241 p. £16.95, $ 27.95 pbk; £45.00, $ 74.95 hbk (1999). Reviewer: O.Ninnemann (Berlin) MSC: 11-01 11A07 11A15 11A41 11Y05 11D04 11Y11 11D09 11Y16 11D25 11H55 11A55 PDF BibTeX XML Cite \textit{H. Davenport}, The higher arithmetic. An introduction to the theory of numbers. Chapter VIII by J. H. Davenport. 7th ed. Cambridge: Cambridge University Press (1999; Zbl 0958.11002)
Jennings, Derek; Byard, Kevin Qualified residue difference sets with zero. (English) Zbl 0932.11004 Discrete Math. 181, No. 1-3, 283-288 (1998). Reviewer: A.R.Rajwade (Chandigarh) MSC: 11A15 05B10 PDF BibTeX XML Cite \textit{D. Jennings} and \textit{K. Byard}, Discrete Math. 181, No. 1--3, 283--288 (1998; Zbl 0932.11004) Full Text: DOI
Zhu, Wenyu Numbers which are Carmichael numbers and strong pseudoprimes to some bases. (Chinese. English summary) Zbl 0884.11004 J. Sichuan Univ., Nat. Sci. Ed. 34, No. 3, 269-275 (1997). Reviewer: Peter Shiu (Loughborough) MSC: 11A15 11A51 11Y11 PDF BibTeX XML Cite \textit{W. Zhu}, J. Sichuan Univ., Nat. Sci. Ed. 34, No. 3, 269--275 (1997; Zbl 0884.11004)
Lemmermeyer, Franz Rational quartic reciprocity. II. (English) Zbl 0878.11040 Acta Arith. 80, No. 3, 273-276 (1997). Reviewer: R.Mollin (Calgary) MSC: 11R16 11A15 PDF BibTeX XML Cite \textit{F. Lemmermeyer}, Acta Arith. 80, No. 3, 273--276 (1997; Zbl 0878.11040) Full Text: DOI arXiv EuDML
Le, Maohua The solvability of the diophantine equation \(D_ 1x^ 2-D_ 2x^ 4=1\). (English) Zbl 0824.11011 Colloq. Math. 68, No. 2, 165-186 (1995). Reviewer: R.J.Stroeker (Rotterdam) MSC: 11D25 11A15 PDF BibTeX XML Cite \textit{M. Le}, Colloq. Math. 68, No. 2, 165--186 (1995; Zbl 0824.11011) Full Text: DOI EuDML
Lemmermeyer, Franz Rational quartic reciprocity. (English) Zbl 0833.11049 Acta Arith. 67, No. 4, 387-390 (1994). Reviewer: R.Mollin (Calgary) MSC: 11R16 11A15 PDF BibTeX XML Cite \textit{F. Lemmermeyer}, Acta Arith. 67, No. 4, 387--390 (1994; Zbl 0833.11049) Full Text: DOI arXiv EuDML
Sun, Zhihong Notes on quartic residue symbol and rational reciprocity laws. (Chinese. English summary) Zbl 0791.11001 J. Nanjing Univ., Math. Biq. 9, No. 1, 92-101 (1992). Reviewer: Zhang Xianke (Beijing) MSC: 11A15 PDF BibTeX XML Cite \textit{Z. Sun}, J. Nanjing Univ., Math. Biq. 9, No. 1, 92--101 (1992; Zbl 0791.11001)
Ming, Luo An elementary proof of a theorem of Bremner. (English) Zbl 0756.11006 Osaka J. Math. 28, No. 3, 747-750 (1991). Reviewer: Ke Zhao (Chengdu) MSC: 11D25 PDF BibTeX XML Cite \textit{L. Ming}, Osaka J. Math. 28, No. 3, 747--750 (1991; Zbl 0756.11006)
Louboutin, Stéphane Norme relative de l’unité fondamentale et 2-rang du groupe des classes de certains corps biquadratiques. (Relative norm of the fundamental unit and 2-rank of the ideal class group of some biquadratic fields). (French) Zbl 0703.11050 Acta Arith. 58, No. 3, 273-288 (1991). Reviewer: S.Louboutin MSC: 11R16 11R29 11R27 PDF BibTeX XML Cite \textit{S. Louboutin}, Acta Arith. 58, No. 3, 273--288 (1991; Zbl 0703.11050) Full Text: DOI EuDML
Cao, Yushu On the Diophantine equation \(X^2=Dy^4+4\). (Chinese. English summary) Zbl 0979.11504 J. Nat. Sci. Heilongjiang Univ. 7, No. 2, 20-23 (1990). MSC: 11D25 11A15 PDF BibTeX XML Cite \textit{Y. Cao}, J. Nat. Sci. Heilongjiang Univ. 7, No. 2, 20--23 (1990; Zbl 0979.11504)
Chuman, Yasuhiro; Ishii, Noburo On the quartic residue of quadratic units of negative norm. (English) Zbl 0628.10004 Math. Jap. 32, 389-420 (1987). Reviewer: F.Halter-Koch MSC: 11A15 11R11 11R27 PDF BibTeX XML Cite \textit{Y. Chuman} and \textit{N. Ishii}, Math. Japon. 32, 389--420 (1987; Zbl 0628.10004)
Lehmer, D. H.; Lehmer, Emma Cyclotomic resultants. (English) Zbl 0615.12022 Math. Comput. 48, 211-216 (1987). Reviewer: A.R.Rajwade MSC: 11T22 11A15 PDF BibTeX XML Cite \textit{D. H. Lehmer} and \textit{E. Lehmer}, Math. Comput. 48, 211--216 (1987; Zbl 0615.12022) Full Text: DOI
Sczech, Robert Dedekind sums and power residue symbols. (English) Zbl 0604.10010 Compos. Math. 59, 89-112 (1986). Reviewer: J.Antoniadis MSC: 11F03 11A15 11R37 11B39 11R11 11R16 PDF BibTeX XML Cite \textit{R. Sczech}, Compos. Math. 59, 89--112 (1986; Zbl 0604.10010) Full Text: Numdam EuDML
Friesen, C.; Spearman, B. K.; Williams, K. S. Another proof of Eisenstein’s law of cubic reciprocity and its supplement. (English) Zbl 0601.10002 Rocky Mt. J. Math. 16, 395-402 (1986). Reviewer: Heima Hayashi (Kumamoto) MSC: 11A15 11R16 PDF BibTeX XML Cite \textit{C. Friesen} et al., Rocky Mt. J. Math. 16, 395--402 (1986; Zbl 0601.10002) Full Text: DOI
Halter-Koch, Franz On the quartic character of certain quadratic units and the representation of primes by binary quadratic forms. (English) Zbl 0599.12003 Rocky Mt. J. Math. 16, 95-102 (1986). Reviewer: K.S.Williams MSC: 11R11 11R27 11A15 11R23 11R37 PDF BibTeX XML Cite \textit{F. Halter-Koch}, Rocky Mt. J. Math. 16, 95--102 (1986; Zbl 0599.12003) Full Text: DOI
Hiramatsu, Toyokazu; Ishii, Noburo Corrections to ”Quartic reciduacity and cusp forms of weight one”. (English) Zbl 0597.12014 Comment. Math. Univ. St. Pauli 35, 111 (1986). MSC: 11R39 11F11 11B39 PDF BibTeX XML Cite \textit{T. Hiramatsu} and \textit{N. Ishii}, Comment. Math. Univ. St. Pauli 35, 111 (1986; Zbl 0597.12014)
Halter-Koch, Franz Konstruktion von Klassenkörpern und Potenzrestkriterien für quadratische Einheiten. (German) Zbl 0586.12008 Manuscr. Math. 54, 453-492 (1986). Reviewer: H.Cohn MSC: 11R37 11A15 11R11 11E16 PDF BibTeX XML Cite \textit{F. Halter-Koch}, Manuscr. Math. 54, 453--492 (1986; Zbl 0586.12008) Full Text: DOI EuDML
Hiramatsu, Toyokazu; Ishii, Noburo Quartic residuacity and cusp forms of weight one. (English) Zbl 0574.12013 Comment. Math. Univ. St. Pauli 34, 91-103 (1985). Reviewer: J.A.Antoniadis MSC: 11R39 11F11 11A15 PDF BibTeX XML Cite \textit{T. Hiramatsu} and \textit{N. Ishii}, Comment. Math. Univ. St. Pauli 34, 91--103 (1985; Zbl 0574.12013)
Williams, Kenneth S.; Friesen, Christian; Howe, Lawrence J. Criteria for biquadratic residuacity modulo a prime \(p\) involving quaternary representations of \(p\). (English) Zbl 0573.10003 Can. J. Math. 37, 337-370 (1985). Reviewer: A. R. Rajwade (Chandigarh) MSC: 11A15 11E20 11R18 11T22 11R29 PDF BibTeX XML Cite \textit{K. S. Williams} et al., Can. J. Math. 37, 337--370 (1985; Zbl 0573.10003) Full Text: DOI
Halter-Koch, Franz An Artin character and representations of primes by binary quadratic forms. III. (English) Zbl 0568.12002 Manuscr. Math. 51, 163-169 (1985). Reviewer: Franz Halter-Koch (Graz) MSC: 11R11 11R37 11A15 11R27 PDF BibTeX XML Cite \textit{F. Halter-Koch}, Manuscr. Math. 51, 163--169 (1985; Zbl 0568.12002) Full Text: DOI EuDML
Kramer, Kenneth Residue properties of certain quadratic units. (English) Zbl 0567.12003 J. Number Theory 21, 204-213 (1985). Reviewer: K.S.Williams MSC: 11R11 11R27 11A15 11R23 11R37 PDF BibTeX XML Cite \textit{K. Kramer}, J. Number Theory 21, 204--213 (1985; Zbl 0567.12003) Full Text: DOI
Ishii, Noburo Cusp forms of weight one, quartic reciprocity and elliptic curves. (English) Zbl 0556.10019 Nagoya Math. J. 98, 117-137 (1985). Reviewer: Noburo Ishii MSC: 11F11 11F33 11R39 14H52 PDF BibTeX XML Cite \textit{N. Ishii}, Nagoya Math. J. 98, 117--137 (1985; Zbl 0556.10019) Full Text: DOI
Cassels, J. W. S. A note on the diophantine equation \(x^ 3+y^ 3+z^ 3=3\). (English) Zbl 0556.10007 Math. Comput. 44, 265-266 (1985). Reviewer: B.Richter MSC: 11D25 PDF BibTeX XML Cite \textit{J. W. S. Cassels}, Math. Comput. 44, 265--266 (1985; Zbl 0556.10007) Full Text: DOI
Baker, Alan A concise introduction to the theory of numbers. (English) Zbl 0554.10001 Cambridge etc.: Cambridge University Press. XIII, 95 p. hbk: £15.00; $ 29.95; pbk: £4.95; $ 9.95 (1984). Reviewer: Bernd Richter (Berlin) MSC: 11-01 11Axx 11D09 11D25 11D61 11J81 11H55 11R11 11R27 PDF BibTeX XML
Kaplan, Pierre; Williams, Kenneth S.; Yamamoto, Yoshihiko An application of dihedral fields to representations of primes by binary quadratic forms. (English) Zbl 0553.10018 Acta Arith. 44, 407-413 (1984). Reviewer: E.Brown MSC: 11E16 11E41 11R11 11R16 11A15 PDF BibTeX XML Cite \textit{P. Kaplan} et al., Acta Arith. 44, 407--413 (1984; Zbl 0553.10018) Full Text: DOI EuDML
Buell, Duncan A.; Hudson, Richard H.; Williams, Kenneth S. Extension of a theorem of Cauchy and Jacobi. (English) Zbl 0551.12014 J. Number Theory 19, 309-340 (1984). Reviewer: A.R.Rajwade MSC: 11T55 11A15 11E20 11T22 PDF BibTeX XML Cite \textit{D. A. Buell} et al., J. Number Theory 19, 309--340 (1984; Zbl 0551.12014) Full Text: DOI
Zantema, H. Global restrictions on ramification in number fields. (English) Zbl 0519.12005 Manuscr. Math. 43, 87-106 (1983). Reviewer: Roelof J. Stroeker (Rotterdam) MSC: 11R21 11R34 11S15 11R16 14F22 11R29 11R09 12G05 11A15 PDF BibTeX XML Cite \textit{H. Zantema}, Manuscr. Math. 43, 87--106 (1983; Zbl 0519.12005) Full Text: DOI EuDML
Hudson, Richard H.; Williams, Kenneth S. On Legendre’s equation \(ax^2 + by^2 + cz^2 = 0\). (English) Zbl 0505.10002 J. Number Theory 16, 100-105 (1983). Reviewer: Roelof J. Stroeker (Rotterdam) MSC: 11A15 11D09 11R11 PDF BibTeX XML Cite \textit{R. H. Hudson} and \textit{K. S. Williams}, J. Number Theory 16, 100--105 (1983; Zbl 0505.10002) Full Text: DOI
Sinha, T. N.; Sareen, S. The Diophantine equation \(ax^ 4+cy^ 4=z^ 2\) with only trivial solutions. (English) Zbl 0526.10013 Math. Stud. 46(1978), No. 2-4, 326-329 (1982). MSC: 11D25 11A15 PDF BibTeX XML Cite \textit{T. N. Sinha} and \textit{S. Sareen}, Math. Stud. 46, No. 2--4, 326--329 (1982; Zbl 0526.10013)
Hudson, Richard H.; Williams, Kenneth S. Congruences for representations of primes by binary quadratic forms. (English) Zbl 0493.10007 Acta Arith. 41, 311-322 (1982). Reviewer: David A. Burgess (Nottingham) MSC: 11A15 11E16 PDF BibTeX XML Cite \textit{R. H. Hudson} and \textit{K. S. Williams}, Acta Arith. 41, 311--322 (1982; Zbl 0493.10007) Full Text: DOI EuDML
Hudson, Richard H.; Williams, Kenneth S. A new formulation of the law of octic reciprocity for primes =+-3 (mod 8) and its consequences. (English) Zbl 0488.10002 Int. J. Math. Math. Sci. 5, 565-584 (1982). MSC: 11A15 11L10 PDF BibTeX XML Cite \textit{R. H. Hudson} and \textit{K. S. Williams}, Int. J. Math. Math. Sci. 5, 565--584 (1982; Zbl 0488.10002) Full Text: DOI EuDML
Davenport, Harold The higher arithmetic. An introduction to the theory of numbers. 5th ed. (English) Zbl 0483.10002 Cambridge etc.: Cambridge University Press. 189 p. hbk: £12.00; pbk: £5.00 (1982). MSC: 11-01 11A41 11A07 11A15 11A55 11D09 11D25 11D04 11H55 11E25 11E41 PDF BibTeX XML
Hudson, Richard H.; Williams, Kenneth S. A new criterion for 7 to be a fourth power (mod p). (English) Zbl 0466.10002 Isr. J. Math. 38, 221-230 (1981). MSC: 11A15 PDF BibTeX XML Cite \textit{R. H. Hudson} and \textit{K. S. Williams}, Isr. J. Math. 38, 221--230 (1981; Zbl 0466.10002) Full Text: DOI
Chowla, Sarvadaman; Cowles, M.; Cowles, J. On the difference of cubes \((\mod p)\). (English) Zbl 0446.10003 Acta Arith. 37, 61-65 (1980). MSC: 11A15 11D25 PDF BibTeX XML Cite \textit{S. Chowla} et al., Acta Arith. 37, 61--65 (1980; Zbl 0446.10003) Full Text: DOI EuDML
Singh, Sahib Bound for the solutions of a Diophantine equation in prime Galois fields. (English) Zbl 0422.10002 Indian J. Pure Appl. Math. 8, 1428-1430 (1977). MSC: 11A15 11D25 PDF BibTeX XML Cite \textit{S. Singh}, Indian J. Pure Appl. Math. 8, 1428--1430 (1977; Zbl 0422.10002)
Lehmer, Emma On some special quartic reciprocity laws. (English) Zbl 0215.06503 Acta Arith. 21, 367-377 (1972). Reviewer: Emma Lehmer MSC: 11A15 11D09 PDF BibTeX XML Cite \textit{E. Lehmer}, Acta Arith. 21, 367--377 (1972; Zbl 0215.06503) Full Text: DOI EuDML
Shiratani, K. Die Diskriminante der Weierstraßschen elliptischen Funktionen und das Reziprozitätsgesetz in besonderen imaginär-quadratischen Zahlkörpern. (German) Zbl 0163.05101 Abh. Math. Semin. Univ. Hamb. 31, 51-61 (1967). Reviewer: Tomio Kubota MSC: 11R11 PDF BibTeX XML Cite \textit{K. Shiratani}, Abh. Math. Semin. Univ. Hamb. 31, 51--61 (1967; Zbl 0163.05101) Full Text: DOI
Davenport, Harold The higher arithmetic. An introduction to the theory of numbers. Übersetzung aus dem Englischen von B. Z. Moroz. Unter Redaktion von Yu. V. Linnik. (Russian) Zbl 0131.03901 Moskau: Verlag ‘Nauka’. Hauptredaktion für physikalisch-mathematische Literatur. 175 S. (1965). MSC: 11-01 11A41 11A07 11A15 11A55 11D09 11D25 11D04 11H55 11E25 11E41 PDF BibTeX XML
Habicht, Walter Ein elementarer Beweis des kubischen Reziprozitätsgesetzes. (German) Zbl 0104.26501 Math. Ann. 139, 343-365 (1960). Reviewer: László Rédei (Szeged) MSC: 11A15 11R16 PDF BibTeX XML Cite \textit{W. Habicht}, Math. Ann. 139, 343--365 (1960; Zbl 0104.26501) Full Text: DOI EuDML
Davenport, Harold The higher arithmetic. An introduction to the theory of numbers. (English) Zbl 0049.30901 London: Hutchinson’s University Library VIII, 172 p. (1952). MSC: 11-01 11A41 11A07 11A15 11A55 11D09 11D25 11D04 11H55 11E25 11E41 PDF BibTeX XML
Skolem, Th. Ein elementares Verfahren zur Herleitung der quadratischen Reziprozitätsgesetze in algebraischen Zahlkörpern. (German) Zbl 0005.24504 Skr. Norske Vid.-Akad., Oslo 1932, No. 2, 1-57 (1932). Reviewer: W. Weber (Göttingen) MSC: 11R11 11R16 11A15 PDF BibTeX XML
Bachmann, P. Elementary number theory. (Niedere Zahlentheorie.) (German) JFM 31.0175.01 Encykl. d. math. Wiss. 1, 555-581 (1900). Reviewer: Wallenberg, Dr. (Charlottenburg) MSC: 11-02 11A05 11A07 11A15 11A25 11A41 11A51 11A55 11D04 11D09 11D25 05B15 PDF BibTeX XML
Goldscheider, F. The reciprocity law for eighth power residues. (Das Reciprocitätsgesetz der achten Potenzreste.) (German) JFM 21.0178.02 Pr. Berlin. Luisenstädt. Realgymn. 29 S. \(4^{\circ}\) (1889). Reviewer: Simon, P., Dr. (Potsdam) MSC: 11A15 11R16 PDF BibTeX XML
Pellet, A.-E. On cubic and biquadratic characters. (Sur les caractères cubiques et biquadratiques.) (French) JFM 21.0178.01 C. R. CVIII, 609-610 (1889). Reviewer: Simon, P., Dr. (Potsdam) MSC: 11A15 11T22 PDF BibTeX XML Cite \textit{A. E. Pellet}, C. R. Acad. Sci., Paris 108, 609--610 (1889; JFM 21.0178.01) Full Text: Gallica
Busche, E. Arithmetical proof of the reciprocity law for biquadratic residues. (Arithmetischer Beweis des Reciprocitätsgesetzes für die biquadratischen Reste.) (German) JFM 18.0147.01 Kronecker J. IC, 261-274 (1886). Reviewer: Simon, P., Dr. (Berlin) MSC: 11A15 PDF BibTeX XML Cite \textit{E. Busche}, J. Reine Angew. Math. 99, 261--274 (1886; JFM 18.0147.01) Full Text: Crelle EuDML
Pépin, Th. On three theorems of Gauss. On some binomial congruences. (Sur trois théorèmes de Gauss. Sur quelques congruences binômes.) (French) JFM 18.0146.03 Rom. Acc. P. d. N. L. XXXVIII, 197-200 (1886); XXXVIII, 201-210 (1886). Reviewer: Simon, P., Dr. (Berlin) MSC: 11A15 PDF BibTeX XML Cite \textit{Th. Pépin}, Rom. Acc. P. d. N. L. 38, 197--200 (1886; JFM 18.0146.03)
Nazimoff, P. S. Application of the theory of elliptic functions to number theory. (Anwendung der Theorie der elliptischen Functionen auf die Theorie der Zahlen.) (Russian) JFM 17.0139.01 Moskau (1885). Reviewer: Wassilieff, A., Dr. (Kazan) MSC: 11-02 11A15 11E12 11E25 11R11 33E05 PDF BibTeX XML
Stieltjes, T. J. jun. A contribution to the theory of cubic and quartic residues. (Bijdrage tot de theorie der derde-en vierde-machts resten.) (Dutch) JFM 14.0123.02 Amst. Versl. en Meded. XVII, 338-417 (1882). Reviewer: van Geer, Prof. (Leiden) MSC: 11A15 PDF BibTeX XML Cite \textit{T. J. Stieltjes jun.}, Versl. en Mededeel. (2) 17, 338--417 (1882; JFM 14.0123.02)
Schwering, K. A study of the fifth power residues and of the numbers built of the fifth roots of unity. (Untersuchung über die fünften Potenzreste und die aus fünften Einheitswurzeln gebildeten ganzen Zahlen.) (German) JFM 14.0122.01 Schlömilch Z. XXVII, 102-119 (1882). Reviewer: Simon, Dr. (Berlin) MSC: 11A15 11R16 11R18 PDF BibTeX XML Cite \textit{K. Schwering}, Schlömilch Z. 27, 102--119 (1882; JFM 14.0122.01)