A classical Diophantine problem and modular forms of weight 3/2

Alter, R., Curtz, T.B., Kubota, K.K.: Remarks and results on congruent numbers. Proc. Third Southeastern Conf. on Combinatorics, Graph Theory and Computing 1972, pp. 27–35Google Scholar

Alter, R.: The congruent number problem. Amer. Math. Monthly87, 43–45 (1980)Google Scholar

Birch, B.J., Swinnerton-Dyer, H.P.F.: Notes on elliptic curves II. J. reine angewandte Math.218, 79–108 (1965)Google Scholar

Birch, B.J., Kuyk, W.: Tables on elliptic curves. In: Modular functions of one variable IV. Lecture Notes in Mathematics, vol. 476, pp. 81–144. Berlin-Heidelberg-New York: Springer 1979Google Scholar

Barrucand, P., Cohn, H.: Note on primes of typex ²+32y ², class number, and residuacity. J. reine angewandte Math.238, 67–70 (1969)Google Scholar

Brown, E.: The class number of\(Q(\sqrt { - p} )\), forp≡1 (mod 8) a prime. Proc. Amer. Math. Soc.31, 381–383 (1972)Google Scholar

Coates, J., Wiles, A.: On the conjecture of Birch and Swinnerton-Dyer. Invent. Math.39, 223–251 (1977)Google Scholar

Cohen, H., Oesterlé, J.: Dimension des espaces de formes modulaires. In: Modular functions of one variable VI. Lecture Notes in Mathematics, vol. 627, pp. 69–78. Berlin-Heidelberg-New York: Springer 1977Google Scholar

Dickson, L.E.: History of the theory of numbers II. Carnegie Institution, Washington, DC (1920) (reprinted by Chelsea, 1966)Google Scholar

Flicker, Y.: Automorphic forms on covering groups ofGL(2). Invent. Math.57, 119–182 (1980)Google Scholar

Jones, B.W.: The arithmetic theory of quadratic forms. Math. Assoc. of Amer., Baltimore, MD 1950Google Scholar

Lagrange, J.: Thèse d'Etat de l'Université de Reims, 1976Google Scholar

Moreno, C.J.: The higher reciprocity laws: an example. J. Number Theory12, 57–70 (1980)Google Scholar

Pizer, A.: On the 2-part of the class number of imaginary quadratic number fields. J. Number Theory8, 184–192 (1976)Google Scholar

Razar, M.: The nonvanishing ofL(1) for certain elliptic curves with no first descents. Amer. J. Math.96, 104–126 (1974)Google Scholar

Razar, M.: A relation between the two-component of the Tate-Shafarevitch group andL(1) for certain elliptic curves. Amer. J. Math.96, 127–144 (1974)Google Scholar

Serre, J-P., Stark, H.M.: Modular forms of weight 1/2. In: Modular functions of one variable VI. Lecture Notes in Mathematics, vol. 627, pp. 27–68. Berlin-Heidelberg-New York: Springer 1977Google Scholar

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

Shimura, G.: Introduction to the arithmetic theory of automorphic functions. Iwanami Shoten and Princeton University Press 1971Google Scholar

Smith, H.J.: Collected Mathematical Papers, Volume 1, Oxford (1894). (reprinted by Chelsea, 1965)Google Scholar

Stephens, N.M.: Congruence Properties of Congruent numbers. Bull. London Math. Soc. pp. 182–184 (1975)Google Scholar

Tate, J.: The arithmetic of elliptic curves. Invent. Math.23, 179–206 (1974)Google Scholar

Tate, J.: Algorithm for determining the type of a singular fiber in an elliptic pencil. In: Modular functions of one variable IV. Lecture Notes in Mathematics, vol. 476, pp. 33–52. Berlin-Heidelberg-New York: Springer 1975Google Scholar

Tate, J.: Number theoretic background. In: Automorphic forms, representations, andL-functions. Proc. Symp. in Pure Math. XXXIII, Part 2, pp. 3–26 (1979)Google Scholar

Waldspurger, J.-L.: Sur les coefficients de Fourier des formes modulaires de poids demi-entier. J. de Math. pures et appliquées60, (4) 375–484 (1981)Google Scholar

Guy, R.K.: Unsolved problems. Amer. Math. Monthly88, 758–761 (1981)Google Scholar