Applications of special functions for the general linear group to number theory
Séminaire Delange-Pisot-Poitou. Théorie des nombres (1976-1977)
- Volume: 18, Issue: 2, page 1-16
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topTerras, Audrey. "Applications of special functions for the general linear group to number theory." Séminaire Delange-Pisot-Poitou. Théorie des nombres 18.2 (1976-1977): 1-16. <http://eudml.org/doc/110978>.
@article{Terras1976-1977,
author = {Terras, Audrey},
journal = {Séminaire Delange-Pisot-Poitou. Théorie des nombres},
language = {eng},
number = {2},
pages = {1-16},
publisher = {Secrétariat mathématique},
title = {Applications of special functions for the general linear group to number theory},
url = {http://eudml.org/doc/110978},
volume = {18},
year = {1976-1977},
}
TY - JOUR
AU - Terras, Audrey
TI - Applications of special functions for the general linear group to number theory
JO - Séminaire Delange-Pisot-Poitou. Théorie des nombres
PY - 1976-1977
PB - Secrétariat mathématique
VL - 18
IS - 2
SP - 1
EP - 16
LA - eng
UR - http://eudml.org/doc/110978
ER -
References
top- [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. Zbl0324.12005MR392913
- [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). Zbl0256.32001MR369750
- [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). Zbl0213.47201MR204533
- [4] Born ( M.) and Huang ( K.). - Dynamical theory of crystal lattices. - London, OxfordUniversity Press, 1956. Zbl0057.44601
- [5] Davenport ( H.). - Multiplicative number theory. - Chicago, Markham, 1967 (Lectures in advanced Mathematics, 1). Zbl0159.06303MR217022
- [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. Zbl0092.00102MR104550
- [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. Zbl0177.50601MR236325
- [9] Herz ( C.S.). - Bessel functions of matrix argument, Annals of Math., Series 2, t. 61, 1955, p. 474-523. Zbl0066.32002MR69960
- [10] Koecher ( M.). - Über Dirichlet-Reihen mit Funktionalgleichung, J. reine und angew. Math., t. 192, 1953, p. 1-23. Zbl0053.05501MR57907
- [11] Lang ( S.). - Algebraic number theory. - Reading, Addison-Wesley, 1970. Zbl0211.38404MR282947
- [12] Langlands ( R.). - On the functional equations satisfied by Eisenstein series. - Berlin, Springer-Verlag, 1976 (Lecture Notes in Mathematics, 544). Zbl0332.10018MR579181
- [13] Lavrik ( A.F.). - Approximate functional equations for Dirichlet functions, Math. U. S. S. R.-Isvestija, t. 2, 1968, p. 129-179. Zbl0188.10403MR223313
- [14] Lavrik ( A.F.). - An approximate functional equation for the Dirichlet L-function, Trans. Moscow Math. Soc., t. 18, 1968, p. 101-115. Zbl0195.33301MR236126
- [15] Maass ( H.). - Siegel's modular forms and Dirichlet series. - Berlin, Springer-Verlag, 1971 (Lecture Notes in Mathematics, 216). Zbl0224.10028MR344198
- [16] Maass ( H.). - On modular functions of one complex variable. - Bombay, Tata Institute, 1964 (Tata Institute of fundamental Research. Lectures on Mathematics, 29). Zbl0254.10018MR218305
- [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. Zbl0080.26601MR103183
- [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. Zbl0002.33001
- [20] Resnikoff ( H.). - Automorphic forms of singular weight are singular forms, Math. Annalen, t. 215, 1975, p. 173-193. Zbl0304.32019MR382177
- [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. Zbl0072.08201MR88511
- [23] Siegel ( C.L.). - Lectures on advanced analytic number theory. - Bombay, Tata Institute, 1957 (Tata Institute of fundamental Research. Lectures in Mathematics, 23). Zbl0278.10001MR262150
- [24] Siegel ( C.L.). - AnalytischeZahlentheorie. - Göttingen, Mathematisches Institut, 1963/64 (Universität Göttingen). Zbl0226.10003
- [25] Siegel ( C.L.). - Gesammelte Abhandlungen. - Berlin, Springer-Verlag, 1966. Zbl0143.00101MR197270
- [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). Zbl0208.06102MR252350
- [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. Zbl0348.12017
- [28] Stark ( H. ). - Hilbert's 12th problem and L-series (to appear). Zbl0378.12007
- [29] Terras ( A.). - A generalization of Epstein's zeta function, Nagoya math. J., t. 42, 1971, p. 173-188. Zbl0212.07702MR286761
- [30] Terras ( A.). - Functional equations of generalized Epstein zeta functions in several variables, Nagoya math. J., t. 44, 1971, p. 89-95. Zbl0212.07801MR289430
- [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. Zbl0274.10039MR323735
- [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. Zbl0303.10029MR369267
- [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. Zbl0282.10025MR396434
- [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. Zbl0295.12006MR417132
- [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. Zbl0306.12006MR435042
- [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. Zbl0359.10024
- [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. Zbl0063.08199MR15393
- [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. Zbl0326.33010MR402145
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