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Identities involving the coefficients of a class of Dirichlet series. III


Author: Bruce C. Berndt
Journal: Trans. Amer. Math. Soc. 146 (1969), 323-348
MSC: Primary 10.41
DOI: https://doi.org/10.1090/S0002-9947-1969-0252330-1
MathSciNet review: 0252330
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  • [1] Bruce C. Berndt, Identities involving the coefficients of a class of Dirichlet series. I, Trans. Amer. Math. Soc. 137 (1969), 345-359. MR 0260685 (41:5309)
  • [2] -, Identities involving the coefficients of a class of Dirichlet series. II, Trans. Amer. Math. Soc. 137 (1969), 361-374. MR 0236360 (38:4656)
  • [3] -, Generalised Dirichlet series and Hecke's functional equation, Proc. Edinburgh Math. Soc. 15 (1967), 309-313.
  • [4] S. Bochner, Some properties of modular relations, Ann. of Math. 53 (1951), 332-363. MR 0047719 (13:920b)
  • [5] K. Chandrasekharan and Raghavan Narasimhan, Hecke's functional equation and arithmetical identities, Ann. of Math. 74 (1961), 1-23. MR 0171761 (30:1988)
  • [6] -, Hecke's functional equation and the average order of arithmetical functions, Acta Arith. 6 (1961), 487-503.
  • [7] -, Functional equations with multiple gamma factors and the average order of arithmetical functions, Ann. of Math. 76 (1962), 93-136. MR 0140491 (25:3911)
  • [8] E. T. Copson, Theory of functions of a complex variable, Clarendon Press, Oxford, 1935.
  • [9] A. L. Dixon and W. L. Ferrar, Some summations over the lattice points of a circle (I), Quart. J. Math. Oxford Ser. 5 (1934), 48-63.
  • [10] A. Erdélyi, Editor, Tables of integral transforms, Vol. 1, McGraw-Hill, New York, 1954.
  • [11] I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, Academic Press, New York, 1965. MR 1773820 (2001c:00002)
  • [12] G. H. Hardy, On the expression of a number as the sum of two squares, Quart. J. Math. Oxford Ser. 46 (1915), 263-283.
  • [13] E. W. Hobson, The theory of functions of a real variable, Vol. II, 2nd ed., Cambridge Univ. Press, Cambridge, 1926.
  • [14] N. S. Koshliakov, Application of the theory of sumformulae to the investigation of a class of one-valued analytical functions in the theory of numbers, Messenger of Math. 58 (1929), 1-23.
  • [15] J. E. Littlewood, Lectures on the theory of functions, Oxford Univ. Press, Oxford, 1944. MR 0012121 (6:261f)
  • [16] G. Szegö, Beiträge zur Theorie der Laguerreschen Polynome. II. Zahlentheoretische Anwendungen, Math. Z. 25 (1926), 388-404. MR 1544819
  • [17] E. C. Titchmarsh, The theory of functions, 2nd ed., Clarendon Press, Oxford, 1939. MR 0197687 (33:5850)
  • [18] G. N. Watson, Theory of Bessel functions, 2nd ed., Cambridge Univ. Press, Cambridge, 1944. MR 0010746 (6:64a)

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DOI: https://doi.org/10.1090/S0002-9947-1969-0252330-1
Article copyright: © Copyright 1969 American Mathematical Society

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