Identities involving the coefficients of a class of Dirichlet series. I
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- by Bruce C. Berndt
- Trans. Amer. Math. Soc. 137 (1969), 345-359
- DOI: https://doi.org/10.1090/S0002-9947-1969-99934-2
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Part II: Trans. Amer. Math. Soc. (1969), 361-374
References
- T. M. Apostol and Abe Sklar, The approximate functional equation of Hecke’s Dirichlet series, Trans. Amer. Math. Soc. 86 (1957), 446–462. MR 94319, DOI 10.1090/S0002-9947-1957-0094319-3
- S. Bochner, Some properties of modular relations, Ann. of Math. (2) 53 (1951), 332–363. MR 47719, DOI 10.2307/1969546
- K. Chandrasekharan and Raghavan Narasimhan, Hecke’s functional equation and arithmetical identities, Ann. of Math. (2) 74 (1961), 1–23. MR 171761, DOI 10.2307/1970304
- K. Chandrasekharan and Raghavan Narasimhan, Functional equations with multiple gamma factors and the average order of arithmetical functions, Ann. of Math. (2) 76 (1962), 93–136. MR 140491, DOI 10.2307/1970267
- K. Chandrasekharan and Raghavan Narasimhan, The approximate functional equation for a class of zeta-functions, Math. Ann. 152 (1963), 30–64. MR 153643, DOI 10.1007/BF01343729 E. T. Copson, Theory of functions of a complex variable, Clarendon Press, Oxford, 1935. Erich Hecke, Dirichlet series, Planographed Lecture Notes, Princeton Institute for Advanced Study, Edwards Brothers, Ann Arbor, Mich., 1938.
- J. E. Littlewood, Lectures on the Theory of Functions, Oxford University Press, 1944. MR 0012121 A. Oppenheim, Some identities in the theory of numbers, Proc. London Math. Soc. (2) 26 (1927), 295-350.
- Hans-Egon Richert, Über Dirichletreihen mit Funktionalgleichung, Acad. Serbe Sci. Publ. Inst. Math. 11 (1957), 73–124 (German). MR 92816 E. C. Titchmarsh, Theory of Fourier integrals, 2nd ed., Clarendon Press, Oxford, 1948. G. Voronoi, Sur une fonction transcendante et ses applications à la sommation de quelques séries, Ann. Sci. École Norm. Sup. (3) 21 (1904), 207-267, 459-533.
- G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746
- A. Zygmund, On trigonometric integrals, Ann. of Math. (2) 48 (1947), 393–440. MR 21612, DOI 10.2307/1969179
Bibliographic Information
- © Copyright 1969 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 137 (1969), 345-359
- MSC: Primary 30.24; Secondary 39.00
- DOI: https://doi.org/10.1090/S0002-9947-1969-99934-2
- MathSciNet review: 0236360