Bulletin of the American Mathematical Society

MathSciNet review: 1567213
Full text of review: PDF   This review is available free of charge.
Book Information:

Author: Serge Lang
Title: Introduction to modular forms
Additional book information: A Series of Comprehensive Studies in Mathematics, No. 222, Springer-Verlag, Berlin and New York, 1976, ix + 261 pp.

Walter L. Baily Jr., Introductory lectures on automorphic forms, Kanô Memorial Lectures, No. 2, Iwanami Shoten Publishers, Tokyo; Princeton University Press, Princeton, N.J., 1973. MR 0369750

A. Borel, S. Chowla, C. S. Herz, K. Iwasawa, and J.-P. Serre, Seminar on complex multiplication, Lecture Notes in Mathematics, No. 21, Springer-Verlag, Berlin-New York, 1966. Seminar held at the Institute for Advanced Study, Princeton, N.J., 1957-58. MR 0201394

Armand Borel and George D. Mostow (eds.), Proceedings of Symposia in Pure Mathematics. Vol. IX: Algebraic groups and discontinuous subgroups, American Mathematical Society, Providence, R.I., 1966. MR 0202512

4.

A. Borel and W. Casselman, Automorphic forms, representations and L-functions, Proc. Sympos. Pure Math., vol. 33, Amer. Math. Soc., Providence, R. I., 1979.

Felix E. Browder (ed.), Mathematical developments arising from Hilbert problems, Proceedings of Symposia in Pure Mathematics, Vol. XXVIII, American Mathematical Society, Providence, R.I., 1976. MR 0419125

Pierre Deligne and Willem Kuyk (eds.), Modular functions of one variable. II, Lecture Notes in Mathematics, Vol. 349, Springer-Verlag, Berlin-New York, 1973. MR 0330050

H. Dym and H. P. McKean, Fourier series and integrals, Probability and Mathematical Statistics, No. 14, Academic Press, New York-London, 1972. MR 0442564

A. Fröhlich (ed.), Algebraic number fields: $L$-functions and Galois properties, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1977. MR 0437486

9.

I. M. Gelfand, M. I. Graev and I. I. Piatetskii-Shapiro, Automorphic functions and representation theory, Saunders, Chicago, Ill., 1969.

10.

E. Hecke, Dirichlet series, modular functions and quadratic forms (IAS Lectures), Edwards Bros., Ann Arbor, Mich., 1938.

11.

K. Imai, Generalization of Hecke's correspondence, Ph.D. Thesis, Univ. of California, San Diego, 1979.

Kenkichi Iwasawa, Lectures on $p$-adic $L$-functions, Annals of Mathematics Studies, No. 74, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. MR 0360526

Joseph Lehner, Discontinuous groups and automorphic functions, Mathematical Surveys, No. VIII, American Mathematical Society, Providence, R.I., 1964. MR 0164033

Stephen Lichtenbaum, Values of zeta-functions, étale cohomology, and algebraic $K$-theory, Algebraic $K$-theory, II: “Classical” algebraic $K$-theory and connections with arithmetic (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972) Lecture Notes in Math., Vol. 342, Springer, Berlin, 1973, pp. 489–501. MR 0406981

Hans Maass, Lectures on modular functions of one complex variable, Tata Institute of Fundamental Research Lectures on Mathematics, No. 29, Tata Institute of Fundamental Research, Bombay, 1964. Notes by Sunder Lal. MR 0218305

Hans Maass, Siegel’s modular forms and Dirichlet series, Lecture Notes in Mathematics, Vol. 216, Springer-Verlag, Berlin-New York, 1971. Dedicated to the last great representative of a passing epoch. Carl Ludwig Siegel on the occasion of his seventy-fifth birthday. MR 0344198

Philip M. Morse and Herman Feshbach, Methods of theoretical physics. 2 volumes, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1953. MR 0059774

J.-P. Serre, A course in arithmetic, Graduate Texts in Mathematics, No. 7, Springer-Verlag, New York-Heidelberg, 1973. Translated from the French. MR 0344216

A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. (N.S.) 20 (1956), 47–87. MR 88511

Goro Shimura, Introduction to the arithmetic theory of automorphic functions, Kanô Memorial Lectures, No. 1, Iwanami Shoten Publishers, Tokyo; Princeton University Press, Princeton, N.J., 1971. Publications of the Mathematical Society of Japan, No. 11. MR 0314766

Takuro Shintani, On evaluation of zeta functions of totally real algebraic number fields at non-positive integers, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 23 (1976), no. 2, 393–417. MR 427231

Carl Ludwig Siegel, Gesammelte Abhandlungen. Bände I, II, III, Springer-Verlag, Berlin-New York, 1966 (German). Herausgegeben von K. Chandrasekharan und H. Maass. MR 0197270

C. L. Siegel, Topics in complex function theory. Vol. I, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. Elliptic functions and uniformization theory; Translated from the German by A. Shenitzer and D. Solitar; With a preface by Wilhelm Magnus; Reprint of the 1969 edition; A Wiley-Interscience Publication. MR 1008930

H. M. Stark, The analytic theory of algebraic numbers, Bull. Amer. Math. Soc. 81 (1975), no. 6, 961–972. MR 444611, DOI 10.1090/S0002-9904-1975-13873-0

H. M. Stark, $L$-functions at $s=1$. III. Totally real fields and Hilbert’s twelfth problem, Advances in Math. 22 (1976), no. 1, 64–84. MR 437501, DOI 10.1016/0001-8708(76)90138-9

Audrey Terras, Applications of special functions for the general linear group to number theory, Séminaire Delange-Pisot-Poitou, 18e année: 1976/77, Théorie des nombres, Fasc. 2, Secrétariat Math., Paris, 1977, pp. Exp. No. 23, 16. MR 551347

Nolan R. Wallach, Symplectic geometry and Fourier analysis, Lie Groups: History, Frontiers and Applications, Vol. V, Math Sci Press, Brookline, Mass., 1977. With an appendix on quantum mechanics by Robert Hermann. MR 0488148

André Weil, Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann. 168 (1967), 149–156 (German). MR 207658, DOI 10.1007/BF01361551

1.

W. Baily, Introductory lectures on automorphic forms, Princeton Univ. Press, Princeton, N. J., 1973. MR 0369750

2.

A. Borel et al., Seminar on complex multiplication, Lecture Notes in Math., vol. 21, Springer-Verlag, Berlin and New York, 1966. MR 201394

3.

A. Borel and G. Mostow, eds., Algebraic groups and discontinuous subgroups, Proc. Sympos. Pure Math., vol. 9, Amer. Math. Soc., Providence, R. I., 1966. MR 202512

4.

A. Borel and W. Casselman, Automorphic forms, representations and L-functions, Proc. Sympos. Pure Math., vol. 33, Amer. Math. Soc., Providence, R. I., 1979.

5.

F. Browder, (ed.), Mathematical developments arising from Hilbert's problems, Proc. Sympos. Pure Math., vol. 28, Amer. Math. Soc., Providence, R. I., 1976. MR 419125

6.

P. Deligne et al., eds., Modular functions of one variable I-VI, Lecture Notes in Math., vols. 320, 349, 350, 476, 601, 627, Springer-Verlag, Berlin and New York, 1973, 1975, 1977. MR 330050

7.

H. Dym and H. P. McKean, Fourier series and integrals, Academic Press, New York, 1972. MR 442564

8.

A. Fröhlich, ed., Algebraic number fields (L-functions and Galois properties), Academic Press, New York, 1977. MR 437486

9.

I. M. Gelfand, M. I. Graev and I. I. Piatetskii-Shapiro, Automorphic functions and representation theory, Saunders, Chicago, Ill., 1969.

10.

E. Hecke, Dirichlet series, modular functions and quadratic forms (IAS Lectures), Edwards Bros., Ann Arbor, Mich., 1938.

11.

K. Imai, Generalization of Hecke's correspondence, Ph.D. Thesis, Univ. of California, San Diego, 1979.

12.

K. Iwasawa, On p-adic L-functions, Princeton Univ. Press, Princeton, N. J., 1972. MR 360526

13.

J. Lehner, Discontinuous groups and automorphic functions, Mathematical Surveys, no. 8, Amer. Math. Soc., Providence, R. I., 1964. MR 164033

14.

S. Lichtenbaum, Values of zeta-functions, étale cohomology, and algebraic K-theory, (preprint). MR 406981

15.

H. Maass, Lectures on modular functions of one complex variable, Tata Institute, Bombay, 1964. MR 218305

16.

H. Maass, Siegel's modular forms and Dirichlet series, Lecture Notes in Math., vol. 216, Springer-Verlag, Berlin and New York, 1971. MR 344198

17.

P. M. Morse and H. Feshbach, Methods of theoretical physics I, II, McGraw-Hill, New York, 1952, 1953. MR 59774

18.

J.-P. Serre, A course in arithmetic, Springer-Verlag, Berlin and New York, 1970. MR 344216

19.

A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. 20 (1956), 47-87. MR 88511

20.

G. Shimura, Arithmetic theory of automorphic forms and functions, Princeton Univ. Press, Princeton, N. J., 1971. MR 314766

21.

T. Shintani, On evaluation of zeta functions of totally real algebraic number fields at non-positive integers, J. Fac. Sci. Univ. Tokyo, Sec. IA 23 (1976), 393-417. MR 427231

22.

C. L. Siegel, Gesammelte Abhandlungen, Springer-Verlag, Berlin and New York, 1966. MR 197270

23.

C. L. Siegel, Topics in complex function theory, Vols. I, II, III, Wiley, New York, 1969-1971. MR 1008930

24.

H. M. Stark, The analytic theory of algebraic numbers, Bull. Amer. Math. Soc. 81 (1975), 961-972. MR 444611

25.

H. M. Stark, L-functions at s = 1, I, II, III, IV, Advances in Math. 7 (1971), 301-343; 17 (1975), 60-92; 22 (1976), 64-84 (to appear). MR 437501

26.

A. Terras, Applications of special functions for the general linear group to number theory, Sém. Delange-Pisot-Poitou, 1977, exp. 23. MR 551347

27.

N. Wallach, Symplectic geometry and Fourier analysis, Math. Sci. Press, Brookline, Mass., 1977. MR 488148

28.

A. Weil, Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichung, Math. Ann. 168 (1967), 149-156. MR 207658