The Life and Work of  R. A. Rankin (1915-2001)

The Life and Work of R. A. Rankin (1915-2001)

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by Bruce C. Berndt , Winfried Kohnen , Ken Ono

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@MISC{Berndt_thelife,
    author = {Bruce C. Berndt and Winfried Kohnen and Ken Ono},
    title = {The Life and Work of R. A. Rankin (1915-2001)},
    year = {}
}

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Abstract

decades, one of the world’s foremost experts in modular forms, died on January 27, 2001 in Glasgow at the age of 85. He was one of the founding editors of The Ramanujan Journal. For this and the next issue of the The Ramanujan Journal, many well-known mathematicians have prepared articles in Rankin’s memory. In this opening paper, we provide a short biography of Rankin and discuss some of his major contributions to mathematics. At the conclusion of this article, we provide a complete list of Rankin’s doctoral students and a complete bibliography of all of Rankin’s writings divided into

Citations

233	conjecture de Weil I - Deligne, La - 1974
155	The Theory of Jacobi Forms - Eichler, Zagier - 1985
121	The lost notebook and other unpublished papers. With an introduction by George E - Ramanujan - 1988
105	The New Book of Prime Number Records - Ribenboim - 1995
78	les courbes algébriques et les variétés qui s’en déduisent. Pub. Inst. Math. Strasbourg 7 - Weil, Sur - 1948
75	Modular forms and functions - Rankin - 1977
69	Notebooks (2 volumes), Tata Institute of Fundamental Research - Ramanujan - 1957
69	On the estimation of Fourier coefficients of modular forms - Selberg - 1965
65	Introduction to Modular Forms - Lang - 1976
61	Hecke operators on Γ0(m - Atkin, Lehner - 1970
52	Automorphic Functions - Ford
44	Sums involving the values at negative integers of L-functions of quadratic character - Cohen - 1975
37	Contributions to the theory of Ramanujan’s function τ(n) and similar arithmetical functions. II, The order of Fourier coefficients of integral modular forms - Rankin
30	Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions - Milne
29	The packing of equal spheres - Rogers - 1958
28	On the holomorphy of certain Dirichlet series - Shimura
25	Ramanujan’s unpublished manuscript on the partition and tau functions with proofs and commentary, The Andrews Festschrift (Maratea - Berndt, Ono - 1998
25	Automorphic pseudodifferential operators, Algebraic Aspects of Integrable Systems - Cohen, Manin, et al. - 1997
25	Discontinuous Groups and Automorphic Functions - Lehner
25	The construction of automorphic forms from the derivatives of given forms - Rankin - 1957
24	The difference between consecutive prime numbers - Rankin - 1940
23	Ramanujan - Berndt, Rankin - 1995
23	The Rankin-Selberg method: a survey, in: “Number theory, trace formulas and discrete groups” (Symposium in honor of A. Selberg) p - Bump - 1989
22	Primes in short intervals - Maier - 1985
20	The difference of consecutive primes - Erdős - 1940
20	Modular forms whose Fourier coefficients involve zeta functions of quadratic fields. Modular forms of one variable VI, Springer Verlag LNM 627, 105–169 - Zagier - 1977
18	Combinatorics and Ramanujan’s “lost” notebook, Surveys in combinatorics 1985 - Andrews - 1985
15	Swinnerton-Dyer On the zeros of Eisenstein series - Rankin, F - 1970
12	Bemerkungen über eine Dirichletsche Reihe, die mit der Theorie der Modulformen nahe verbunden ist - Selberg
11	Newforms and functional equations - Li - 1975
11	A Campanological Problem in Group Theory - Rankin - 1948
11	A proof of the Kac-Wakimoto affine denominator formula for the strange series - Zagier - 2000
9	On automorphic forms on GL2 and Hecke operators - Miyake - 1971
9	Symmetric power L-functions for GL(2). In Elliptic curves and related topics - Shahidi - 1994
8	Ramanujan: essays and surveys - Berndt, Rankin - 2001
8	The minimum value of quadratic forms and the closest packing of spheres - Blichfeldt - 1929
8	An Overview of the Kepler Conjecture, preprint math.MG/9811071 - Hales
8	Unusually large gaps between consecutive primes - Maier, Pomerance - 1990
8	Very large gaps between consecutive primes - Pintz - 1997
7	Formulas of Ramanujan for the power series coefficients of certain quotients - Berndt, Bialek, et al.
6	Theorie der Eisensteinschen Reihen höherer Stufe und ihre Anwendung auf Funktionentheorie und Arithmetik - Hecke - 1927
6	Mathematische Werke, Vandenhoeck - Hecke - 1983
5	On the closest packing of spheres in n dimensions - Rankin - 1947
5	The scalar product of modular forms - Rankin - 1952
5	Lattice subgroups of free congruence groups - Rankin - 1967
5	Ramanujan’s manuscripts and notebooks - Rankin - 1982
4	On the numbers of representations of a number as a sum of 2r squares, where 2r does not exceed eighteen - Glaisher - 1907
4	On the coefficients in the expansions of certain modular functions - Hardy, Ramanujan - 1918
4	Representations of integers as sums of squares - Ono
4	Zur analytischen Theorie der Grenzkreisgruppen - Petersson - 1938