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A cuspidal class number formula for the modular curves \(X_1(N)\). (English) Zbl 0426.12003


MSC:

11R23 Iwasawa theory
14H45 Special algebraic curves and curves of low genus
11F03 Modular and automorphic functions
11R27 Units and factorization
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
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References:

[1] Iwasawa, K.: A class number formula for cyclotomic fields. Ann. Math.76, 171-179 (1962) · Zbl 0125.02003 · doi:10.2307/1970270
[2] Klimek, P.: Thesis, Berkeley 1975
[3] Kubert, D.: Quadratic relations for generators of units in the modular function field. Math. Ann.225, 1-20 (1977) · Zbl 0331.10011 · doi:10.1007/BF01364888
[4] Kubert, D.: The universal ordinary distribution. Bull. Soc. Math. France107, 179-202 (1979) · Zbl 0409.12021
[5] Kubert, D., Lang, S.: Modular units (in preparation) · Zbl 0331.10012
[6] Kubert, D., Lang, S.: Units in the modular function field. I. Math. Ann.218, 67-96 (1975) · Zbl 0311.14005 · doi:10.1007/BF01350068
[7] Kubert, D., Lang, S.: Units in the modular function field. II. A full set of units. Math. Ann.218, 175-189 (1975) · Zbl 0311.14005 · doi:10.1007/BF01370818
[8] Kubert, D., Lang, S.: Units in the modular function field. III. Distribution relations. Math. Ann.218, 273-285 (1975) · Zbl 0311.14005 · doi:10.1007/BF01349700
[9] Kubert, D., Lang, S.: Units in the modular function field. IV. The Siegel functions are generators. Math. Ann.227, 223-242 (1977) · Zbl 0345.10012 · doi:10.1007/BF01361857
[10] Kubert, D., Lang, S.: Distributions on toroidal groups. Math. Z.148, 33-51 (1976) · Zbl 0324.10021 · doi:10.1007/BF01187867
[11] Kubert, D., Lang, S.: Thep-primary component of the cuspidal divisor class group on the modular curveX(p). Math. Ann.234, 25-44 (1978) · Zbl 0371.12025 · doi:10.1007/BF01409337
[12] Kubert, D., Lang, S.: Stickelberger ideals. Math. Ann.237, 203-212 (1978) · Zbl 0379.12009 · doi:10.1007/BF01420176
[13] Kubert, D., Lang, S.: The index of Stickelberger ideals of order 2 and cuspidal class numbers. Math. Ann.237, 213-232 (1978) · Zbl 0379.12010 · doi:10.1007/BF01420177
[14] Lang, S.: Introduction to modular forms. Berlin, Heidelberg, New York: Springer 1976 · Zbl 0344.10011
[15] Lang, S.: Cyclotomic fields. Berlin, Heidelberg, New York: Springer 1978 · Zbl 0395.12005
[16] Sinnott, W.: On the Stickelberger ideal and the circular units of a cyclotomic field. Ann. Math.108, 107-134 (1978) · Zbl 0395.12014 · doi:10.2307/1970932
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