Book Review
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MathSciNet review:
1566783
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Book Information:
Author:
Hans Rademacher
Title:
Topics in analytic number theory
Additional book information:
Die Grundlehren der math. Wissenschaften, Band 169, Springer-Verlag, Berlin, 1973, ix+320 pp.
1. H. L. Alder, Partition identities—from Euler to the present, Amer. Math. Monthly 76 (1969), 733-746. MR 41 #8366.
George E. Andrews, On the general Rogers-Ramanujan theorem, Memoirs of the American Mathematical Society, No. 152, American Mathematical Society, Providence, R.I., 1974. MR 0364082
S. Chowla, Remarks on class-invariants and related topics, Calcutta Math. Soc. Golden Jubilee Commemoration Vol. (1958/59), Part II, Calcutta Math. Soc., Calcutta, 1963, pp. 361–372. MR 0154846
Pierre Deligne and Jean-Pierre Serre, Formes modulaires de poids $1$, Ann. Sci. École Norm. Sup. (4) 7 (1974), 507–530 (1975) (French). MR 379379
Marvin Isadore Knopp, Fourier series of automorphic forms of non-negative dimension, Illinois J. Math. 5 (1961), 18–42. MR 122804
Willem Kuyk (ed.), Modular functions of one variable. I, Lecture Notes in Mathematics, Vol. 320, Springer-Verlag, Berlin-New York, 1973. MR 0323723
C. Meyer, Über einige Anwendungen Dedekindscher Summen, J. Reine Angew. Math. 198 (1957), 143–203 (German). MR 104643, DOI 10.1515/crll.1957.198.143
Hans Petersson, Über die Entwicklungskoeffizienten der automorphen Formen, Acta Math. 58 (1932), no. 1, 169–215 (German). MR 1555346, DOI 10.1007/BF02547776
9. Hans A. Rademacher, On the transformation of $łog \eta(\tau)$, J. Indian Math. Soc. 19 (1955), 25-30. MR 17, 15.
H. Rademacher, Some remarks on certain generalized Dedekind sums, Acta Arith. 9 (1964), 97–105. MR 163873, DOI 10.4064/aa-9-1-97-105
11. Hans A. Rademacher, On the partition function p (n), Proc. London Math. Soc. (2) 43 (1937), 241-254.
Hans Rademacher, The Fourier Coefficients of the Modular Invariant J($\tau$), Amer. J. Math. 60 (1938), no. 2, 501–512. MR 1507331, DOI 10.2307/2371313
Hans Rademacher, Trends in research: the analytic number theory, Bull. Amer. Math. Soc. 48 (1942), 379–401. MR 6205, DOI 10.1090/S0002-9904-1942-07679-8
Hans Rademacher and Emil Grosswald, Dedekind sums, The Carus Mathematical Monographs, No. 16, Mathematical Association of America, Washington, D.C., 1972. MR 0357299
Hans Rademacher and Herbert S. Zuckerman, On the Fourier coefficients of certain modular forms of positive dimension, Ann. of Math. (2) 39 (1938), no. 2, 433–462. MR 1503417, DOI 10.2307/1968796
C. L. Siegel, Topics in complex function theory. Vol. III, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1989. Abelian functions and modular functions of several variables; Translated from the German by E. Gottschling and M. Tretkoff; With a preface by Wilhelm Magnus; Reprint of the 1973 original; A Wiley-Interscience Publication. MR 1013364
Carl Ludwig Siegel, Lectures on advanced analytic number theory, Tata Institute of Fundamental Research Lectures on Mathematics, No. 23, Tata Institute of Fundamental Research, Bombay, 1965. Notes by S. Raghavan. MR 0262150
Carl Ludwig Siegel, A simple proof of $\eta (-1/\tau )=\eta (\tau )\sqrt {}\tau /i$, Mathematika 1 (1954), 4. MR 62774, DOI 10.1112/S0025579300000462
André Weil, Sur une formule classique, J. Math. Soc. Japan 20 (1968), 400–402 (French). MR 224556, DOI 10.2969/jmsj/02010400
Herbert S. Zuckerman, On the coefficients of certain modular forms belonging to subgroups of the modular group, Trans. Amer. Math. Soc. 45 (1939), no. 2, 298–321. MR 1501993, DOI 10.1090/S0002-9947-1939-1501993-X
Herbert S. Zuckerman, On the expansions of certain modular forms of positive dimension, Amer. J. Math. 62 (1940), 127–152. MR 1306, DOI 10.2307/2371443
- 1.
- H. L. Alder, Partition identities—from Euler to the present, Amer. Math. Monthly 76 (1969), 733-746. MR 41 #8366.
- 2.
- George E. Andrews, On the general Rogers-Ramanujan theorem, Mem. Amer. Math. Soc. No. 152 (1974). MR 0364082
- 3.
- S. Chowla, Remarks on class-invariants and related topics, Seminar on Complex Multiplication, Institute for Adv. Study, Princeton, N.J., 1957/58, Lecture Notes in Math., no. 21, Springer-Verlag, Berlin and New York, 1966, VI-1 to VI-15. MR 34 #1278. MR 154846
- 4.
- Pierre Deligne and Jean-Pierre Serre, Formes modulaires de poids 1 (to appear). MR 379379
- 5.
- Marvin Isadore Knopp, Fourier series of automorphic forms of non-negative dimension, Illinois J. Math. 5 (1961), 18-42. MR 23 #A137. MR 122804
- 6.
- W. Kuyk, et al. (editors), Modular functions of one variable. I, II, III, Lecture Notes in Math., nos. 320, 349, 350, Springer-Verlag, New York, 1973. MR 323723
- 7.
- C. Meyer, Über einige Anwendungen Dedekindscher Summen, J. Reine Angew. Math. 198 (1957), 143-203. MR 21 #3396. MR 104643
- 8.
- Hans Petersson, Über die Entwicklungskoeffizienten der automorphen formen, Acta Math. 58 (1932), 169-215. MR 1555346
- 9.
- Hans A. Rademacher, On the transformation of $łog \eta(\tau)$, J. Indian Math. Soc. 19 (1955), 25-30. MR 17, 15.
- 10.
- Hans A. Rademacher, Some remarks on certain generalized Dedekind sums, Acta Arith. 9 (1964), 97-105. MR 29 #1172. MR 163873
- 11.
- Hans A. Rademacher, On the partition function p (n), Proc. London Math. Soc. (2) 43 (1937), 241-254.
- 12.
- Hans A. Rademacher, The Fourier coefficients of the modular invariant j (T), Amer. J. Math. 60 (1938), 501-512. MR 1507331
- 13.
- Hans A. Rademacher, Trends in research: the analytic number theory, Bull. Amer. Math. Soc. 48 (1942), 379-401. MR 3, 271. MR 6205
- 14.
- Hans Rademacher and Emil Grosswald, Dedekind sums, Carus Mathematical Monograph, 16, 1972. MR 357299
- 15.
- Hans Rademacher and Herbert S. Zuckerman, On the Fourier coefficients of certain modular forms of positive dimension, Ann. Math. (2) 39 (1938), 433-462. MR 1503417
- 16.
- C. L. Siegel, Topics in complex function theory. Vol. III, Wiley, New York, 1973. MR 1013364
- 17.
- C. L. Siegel, Lectures on advanced analytic number theory, Tata Institute of Fundamental Research, Bombay, 1961. MR 262150
- 18.
- C. L. Siegel, A simple proof of $\eta(-1/\tau)=\eta(\tau)\sqrt{}\tau/i$, Mathematika 1 (1954), 4. MR 16, 16. MR 62774
- 19.
- A. Weil, Sur une formule classique, J. Math. Soc. Japan 20 (1968), 400-402. MR 37 #155. MR 224556
- 20.
- Herbert S. Zuckerman, On the coefficients of certain modular forms belonging to subgroups of the modular group, Trans. Amer. Math. Soc. 45 (1939), 289-321. MR 1501993
- 21.
- Herbert S. Zuckerman, On the expansions of certain modular forms of positive dimension. Amer. J. Math. 62 (1940), 127-152. MR 1, 214. MR 1306
Review Information:
Reviewer:
H. M. Stark
Journal:
Bull. Amer. Math. Soc.
81 (1975), 663-672
DOI:
https://doi.org/10.1090/S0002-9904-1975-13815-8
