Class numbers of quadratic fields and Shimura's correspondence

Jan Nekovář

doi:10.1007/bf01446915

journal article Mar 01, 1990

Class numbers of quadratic fields and Shimura's correspondence

Jan Nekovář

Mathematische Annalen Vol. 287 No. 1 pp. 577-594 · Springer Science and Business Media LLC

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References

24

[1]

Aigner, A.: Weitere Ergebnisse überx 3+y 3=z 3 in quadratischen Körpern. Monatsh. Math.36, 240–252 (1952) 10.1007/bf01297498

[2]

Aigner, A.: Ein zweiter Fall der Unmöglichkeit vonx 3+y 3=z 3 in quadratischen Körpern mit durch 3 teilbarer Klassenzahl. Monatsh. Math.56, 335–338 (1952) 10.1007/bf01302718

[3]

Cassels, J.W.S.: Arithmetic on curves of genus 1, I. J. Reine Angew. Math.202, 52–99 (1959) 10.1515/crll.1959.202.52

[4]

Cassels, J.W.S.: Arithmetic on curves of genus 1, VIII. J. Reine Angew. Math.217, 180–199 (1965) 10.1515/crll.1965.217.180

[5]

Cassels, J.W.S.: Diophantine equations with special reference to elliptic curves. J. Lond. Math. Soc.41, 193–291 (1966) 10.1112/jlms/s1-41.1.193

[6]

Die Klassengruppen quadratischer und kubischer Zahlk�rper und die Selmergruppen gewisser elliptischer Kurven

Gerhard Frey

Manuscripta Mathematica 1975 10.1007/bf01323464

[7]

Fricke, R.: Die elliptischen Funktionen und ihre Anwendungen. Leipzig Berlin: Teuhner 1922

[8]

Fueter, R.: Die diophantische Gleichung ξ3+η3+η3=0. Sitz-Ber. Akad. Wiss. Heidelberg (1913)

[9]

Grosswald, E.: Representations of integers as sums of squares. Berlin Heidelberg New York: Springer 1985 10.1007/978-1-4613-8566-0

[10]

Ireland, K., Rosen, M.: A classical introduction to modern number theory. (Graduate texts in Mathematics vol. 87). Berlin Heidelberg New York: Springer 1982 10.1007/978-1-4757-1779-2

[11]

Milnor, J., Husemoller, D.: Symmetric bilinear forms. Berlin Heidelberg New York: Springer 1983

[12]

Newman, M.: Construction and application of a class of modular functions. Proc. Lond. Math. Soc.7, 334–350 (1957) 10.1112/plms/s3-7.1.334

[13]

Reichardt, H.: Aritmetische Theorie der Kubischen Körper als Radikalkörper. Montash. Math. Phys.40, 323–350 (1933)

[14]

Rubin, K.: Tate-Ŝafareviĉ groups andL-functions of elliptic curves with complex multiplication. Invent. Math.89, 527–560 (1987) 10.1007/bf01388984

[15]

Scholz, A.: Über die Beziehung der Klassenzahlen quadratischer Körper zueinander. J. Reine Angew. Math.166, 201–203 (1932) 10.1515/crll.1932.166.201

[16]

Serre, J.-P.: Modular forms of weight one and Galois representations. Algebraic number fields. A. Fröhlich (ed.) pp. 193–268. London New York: Academic Press 1977

[17]

Serre, J.-P., Stark, H.: Modular forms of weight 1/2. (Lect. Notes Math., vol. 627, pp. 29–68.) Berlin Heidelberg New York: Springer 1977

[18]

Shimura, G.: Introduction to the arithmetic theory of automorphic functions. Princeton: Iwnami Shoten and Princeton Univ. Press 1971

[19]

Shimura, G.: On modular forms of half-integral weight. Ann. Math.97, 440–481 (1973) 10.2307/1970831

[20]

Stevens, G.: Arithmetic of modular curves. Progress in Math. vol. 20. Boston: Birkhäuser 1982 10.1007/978-1-4684-9165-4

[21]

Tate, J.: Algorithm for determining the type of a singular fiber in an elliptic pencil. (Lect. Notes Math., vol. 476, pp. 33–52). Berlin Heidelberg New York: Springer 1975 10.1007/bfb0097582

[22]

Waldspurger, J.-L.: Correspondance de Shimura. J. Math. Pures Appl.59, 1–132 (1980)

[23]

Waldspurger, J.-L.: Sur les coefficients de Fourier des formes modulaires de poids demi-entier. J. Math. Pures Appl.60, 375–484 (1981)

[24]

Numerical tables on elliptic curves. (Lect. Notes Math., vol. 476, pp. 74–144.) Berlin Heidelberg New York: Springer 1975

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Published: Mar 01, 1990
Vol/Issue: 287(1)
Pages: 577-594
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Jan Nekovář

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Jan Nekovář (1990). Class numbers of quadratic fields and Shimura's correspondence. Mathematische Annalen, 287(1), 577-594. https://doi.org/10.1007/bf01446915

Class numbers of quadratic fields and Shimura's correspondence

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