Document Zbl 0274.10039

Bessel series expansions of the Epstein zeta function and the functional equation. (English) Zbl 0274.10039

Trans. Am. Math. Soc. 183, 477-486 (1973).

Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0274.10039

MSC:

11M35	Hurwitz and Lerch zeta functions
33C10	Bessel and Airy functions, cylinder functions, \({}_0F_1\)

Cite Review PDF

Full Text: DOI

References:

[1]	Milton Abramowitz and Irene A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, vol. 55, For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964. · Zbl 0171.38503
[2]	Tetsuya Asai, On a certain function analogous to \?\?\?_{\?}(\?), Nagoya Math. J. 40 (1970), 193 – 211. · Zbl 0213.05701
[3]	P. T. Bateman and E. Grosswald, On Epstein’s zeta function, Acta Arith. 9 (1964), 365 – 373. · Zbl 0128.27004
[4]	Bruce C. Berndt, Identities involving the coefficients of a class of Dirichlet series. V, VI, Trans. Amer. Math. Soc. 160 (1971), 139-156; ibid. 160 (1971), 157 – 167. · Zbl 0228.10024
[5]	Proceedings of Symposia in Pure Mathematics. Vol. IX: Algebraic groups and discontinuous subgroups, Proceedings of the Symposium in Pure Mathematics of the American Mathematical Society held at the University of Colorado, Boulder, Colorado (July 5-August 6, vol. 1965, American Mathematical Society, Providence, R.I., 1966.
[6]	Paul Epstein, Zur Theorie allgemeiner Zetafunktionen. I, Math. Ann. 56 (1903), 614-644. · JFM 34.0461.02
[7]	Erich Hecke, Mathematische Werke, Herausgegeben im Auftrage der Akademie der Wissenschaften zu Göttingen, Vandenhoeck & Ruprecht, Göttingen, 1959 (German). · Zbl 0092.00102
[8]	Carl S. Herz, Bessel functions of matrix argument, Ann. of Math. (2) 61 (1955), 474 – 523. · Zbl 0066.32002 · doi:10.2307/1969810
[9]	William Judson LeVeque, Topics in number theory. Vols. 1 and 2, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1956. · Zbl 0070.03804
[10]	Max Koecher, Ein neuer Beweis der Kroneckerschen Grenzformel, Arch. Math. 4 (1953), 316 – 321 (German). · Zbl 0051.31802 · doi:10.1007/BF01899895
[11]	Atle Selberg and S. Chowla, On Epstein’s zeta-function, J. Reine Angew. Math. 227 (1967), 86 – 110. · Zbl 0166.05204 · doi:10.1515/crll.1967.227.86
[12]	C. L. Siegel, Lectures on quadratic forms, Notes by K. G. Ramanathan. Tata Institute of Fundamental Research Lectures on Mathematics, No. 7, Tata Institute of Fundamental Research, Bombay, 1967. · Zbl 0248.10019
[13]	-, Lectures on advanced analytic number theory, Tata Inst., Bombay, 1961.
[14]	Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton University Press, Princeton, N.J., 1971. Princeton Mathematical Series, No. 32. · Zbl 0232.42007
[15]	Audrey Terras, A generalization of Epstein’s zeta function, Nagoya Math. J. 42 (1971), 173 – 188. · Zbl 0212.07702

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.