Applications of special functions for the general linear group to number theory
Séminaire Delange-Pisot-Poitou. Théorie des nombres, Volume 18 (1976-1977) no. 2, Talk no. 23, 16 p.
@article{SDPP_1976-1977__18_2_A4_0,
     author = {Terras, Audrey},
     title = {Applications of special functions for the general linear group to number theory},
     journal = {S\'eminaire Delange-Pisot-Poitou. Th\'eorie des nombres},
     publisher = {Secr\'etariat math\'ematique},
     volume = {18},
     number = {2},
     year = {1976-1977},
     note = {talk:23},
     zbl = {0373.10016},
     mrnumber = {551347},
     language = {en},
     url = {http://www.numdam.org/item/SDPP_1976-1977__18_2_A4_0}
}
Terras, Audrey. Applications of special functions for the general linear group to number theory. Séminaire Delange-Pisot-Poitou. Théorie des nombres, Volume 18 (1976-1977) no. 2, Talk no. 23, 16 p. http://www.numdam.org/item/SDPP_1976-1977__18_2_A4_0/

[1] Barrucand (P.), Williams (H.), and Baniuk (L.). - A computational technique for determining the class number of a pure cubic field, Math. of Comp., t. 30, 1976, p. 312-323. | MR 392913 | Zbl 0324.12005

[2] Baily (W.). - Introductory lectures on automorphic forms. - Princeton, Princeton University Press, 1973 (Publications of the Mathematical Society of Japan, 12 ; Kano Memorial Lectures, 2). | MR 369750 | Zbl 0256.32001

[3] Borel (A.). - Reduction theory for arithmetic groups ; and Introduction to automorphic forms, "Algebraic groups and discontinuous subgroups", p. 20-25, and p. 199-210. - Providence, American mathematical Society, 1966 (Proceedings of Symposia in pure Mathematics, 9). | MR 204533 | Zbl 0213.47201

[4] Born (M.) and Huang (K.). - Dynamical theory of crystal lattices. - London, Oxford University Press, 1956. | Zbl 0057.44601

[5] Davenport (H.). - Multiplicative number theory. - Chicago, Markham, 1967 (Lectures in advanced Mathematics, 1). | MR 217022 | Zbl 0159.06303

[6] Davenport (H.). - Stanford lectures on selected topics in the geometry of numbers, Stanford University, 1950.

[7] Hecke (E.). - Mathematische Werke. - Göttingen, Vandenhoeck und Ruprecht, 1959. | MR 104550 | Zbl 0092.00102

[8] Helgason (S.). - Lie groups and symmetric spaces, "Battelle Rencontres, 1967, Lectures in Mathematics and physics", p. 1-71. - New York, W. A. Benjamin, 1968. | MR 236325 | Zbl 0177.50601

[9] Herz (C.S.). - Bessel functions of matrix argument, Annals of Math., Series 2, t. 61, 1955, p. 474-523. | MR 69960 | Zbl 0066.32002

[10] Koecher (M.). - Über Dirichlet-Reihen mit Funktionalgleichung, J. reine und angew. Math., t. 192, 1953, p. 1-23. | MR 57907 | Zbl 0053.05501

[11] Lang (S.). - Algebraic number theory. - Reading, Addison-Wesley, 1970. | MR 282947 | Zbl 0211.38404

[12] Langlands (R.). - On the functional equations satisfied by Eisenstein series. - Berlin, Springer-Verlag, 1976 (Lecture Notes in Mathematics, 544). | MR 579181 | Zbl 0332.10018

[13] Lavrik (A.F.). - Approximate functional equations for Dirichlet functions, Math. U. S. S. R.-Isvestija, t. 2, 1968, p. 129-179. | MR 223313 | Zbl 0188.10403

[14] Lavrik (A.F.). - An approximate functional equation for the Dirichlet L-function, Trans. Moscow Math. Soc., t. 18, 1968, p. 101-115. | MR 236126 | Zbl 0195.33301

[15] Maass (H.). - Siegel's modular forms and Dirichlet series. - Berlin, Springer-Verlag, 1971 (Lecture Notes in Mathematics, 216). | MR 344198 | Zbl 0224.10028

[16] Maass (H.). - On modular functions of one complex variable. - Bombay, Tata Institute, 1964 (Tata Institute of fundamental Research. Lectures on Mathematics, 29). | MR 218305 | Zbl 0254.10018

[17] Macbeath (A.M.) and Rogers (C.A.). - Siegel's mean value theorem in the geometry of numbers, Proc. Camb. phil. Soc., t. 54, 1958, p. 139-151. | MR 103183 | Zbl 0080.26601

[18] Montgomery (H.). - Adam's Prize Essay.

[19] Mordell (L.J.). - On Hecke's modular functions, zeta functions, and some other analytic functions in the theory of numbers, Proc. London math. Soc., Series 2, t. 32, 1931, p. 501-556. | Zbl 0002.33001

[20] Resnikoff (H.). - Automorphic forms of singular weight are singular forms, Math. Annalen, t. 215, 1975, p. 173-193. | MR 382177 | Zbl 0304.32019

[21] Resnikoff (H.). - Stable spaces of modular forms (to appear).

[22] Selberg (A.). - Harmonic analysis and discontinuous groups in weakly symmetric riemannian spaces with applications to Dirichlet series, J. Indian math. Soc., t. 20, 1956, p. 47-87. | MR 88511 | Zbl 0072.08201

[23] Siegel (C.L.). - Lectures on advanced analytic number theory. - Bombay, Tata Institute, 1957 (Tata Institute of fundamental Research. Lectures in Mathematics, 23). | MR 262150 | Zbl 0278.10001

[24] Siegel (C.L.). - Analytische Zahlentheorie. - Göttingen, Mathematisches Institut, 1963/64 (Universität Göttingen). | Zbl 0226.10003

[25] Siegel (C.L.). - Gesammelte Abhandlungen. - Berlin, Springer-Verlag, 1966. | MR 197270 | Zbl 0143.00101

[26] Stark (H.). - On the problem of unique factorization in complex quadratic fields, "Number theory", p. 41-56. - Providence, American mathematical Society, 1969 (Proceedings of Symposia in pure Mathematics, 12). | MR 252350 | Zbl 0208.06102

[27] Stark (H.). - Values of L-functions at s = 1 , III : Totally real fields and Hilbert's 12th problem, Advances in Math., t. 22, 1976, p. 64-84. | Zbl 0348.12017

[28] Stark (H. ). - Hilbert's 12th problem and L-series (to appear). | Zbl 0378.12007

[29] Terras (A.). - A generalization of Epstein's zeta function, Nagoya math. J., t. 42, 1971, p. 173-188. | MR 286761 | Zbl 0212.07702

[30] Terras (A.). - Functional equations of generalized Epstein zeta functions in several variables, Nagoya math. J., t. 44, 1971, p. 89-95. | MR 289430 | Zbl 0212.07801

[31] Terras (A.). - Bessel series expansions of the Epstein zeta function and the functional equation, Trans. Amer. math. Soc., t. 183, 1973, p. 477-486. | MR 323735 | Zbl 0274.10039

[32] Terras (A. ). - Fourier coefficients of Eisenstein series of one complex variable for the special linear group, Trans. Amer. math. Soc., t. 205, 1975, p. 97-114. | MR 369267 | Zbl 0303.10029

[33] Terras (A.). - Some formulas for the Riemann zeta function at odd integer argument resulting from Fourier expansions of the Epstein zeta function, Acta Arithm., Warszawa, t. 29, 1975, p. 181-189. | MR 396434 | Zbl 0282.10025

[34] Terras (A.). - The Fourier expansion of Epstein's zeta function for totally real algebraic number fields and some consequences for Dedekind's zeta function, Acta Arithm., Warszawa, t. 30, 1976, p. 187-197. | MR 417132 | Zbl 0295.12006

[35] Terras (A.). - The Fourier expansion of Epstein's zeta function over an algebraic number field and its consequences for algebraic number theory, Acta Arithm., Warszawa, t. 32, 1976, p. 37-53. | MR 435042 | Zbl 0306.12006

[36] Terras (A.). - A relation between ζK(s) and ζK (s - 1) for any algebraic number field K , "Algebraic number fields ( L-functions and Galois properties)"[1975. Durham], p. 475-483. - London, Academic Press, 1977. | Zbl 0359.10024

[37] Terras (A. ). - On a relation between the size of the minima of quadratic forms and the behaviour of Epstein and Dedekind zeta functions in the real part of the critical strip (to appear).

[38] Terras (A.), Purdy (G.), Terras (R.), Williams (H.). - Graphing L-functions of Kronecker symbols in the real part of the critical strip (to appear).

[39] Terras (R.). - On the convergence of the continued fraction for the incomplete gamma function and an algorithm for the Riemann zeta function (to appear).

[40] Terras (R.). - Determination of incomplete gamma functions by recursion in the argument (to appear).

[41] Weil (A.). - Sur quelques résultats de Siegel, Summa Bras. Math., t. 1, 1946, p. 21-39. | MR 15393 | Zbl 0063.08199

[42] James (A.T. ). - Special functions of matrix and single argument in statistics, "Theory and applications of special functions", p. 497-520. - New York, Academic Press, 1975. | MR 402145 | Zbl 0326.33010