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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References | Similar Articles | Additional Information

**[1]**Bruce C. Berndt,*Identities involving the coefficients of a class of Dirichlet series. IV*, Trans. Amer. Math. Soc.**149**(1970), 179–185. MR**260685**, https://doi.org/10.1090/S0002-9947-1970-0260685-5**[2]**Bruce C. Berndt,*Identities involving the coefficients of a class of Dirichlet series. I, II*, Trans. Amer. Math. Soc.**137**(1969), 345–359, 361–374. MR**236360**, https://doi.org/10.1090/S0002-9947-1969-99934-2**[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. (2)**53**(1951), 332–363. MR**47719**, https://doi.org/10.2307/1969546**[5]**K. Chandrasekharan and Raghavan Narasimhan,*Hecke’s functional equation and arithmetical identities*, Ann. of Math. (2)**74**(1961), 1–23. MR**171761**, https://doi.org/10.2307/1970304**[6]**-,*Hecke's functional equation and the average order of arithmetical functions*, Acta Arith.**6**(1961), 487-503.**[7]**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**, https://doi.org/10.2307/1970267**[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*, 6th ed., Academic Press, Inc., San Diego, CA, 2000. Translated from the Russian; Translation edited and with a preface by Alan Jeffrey and Daniel Zwillinger. MR**1773820****[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 University Press, 1944. MR**0012121****[16]**G. Szegö,*Beiträge zur Theorie der Laguerreschen Polynome. II: Zahlentheoretische Anwendungen*, Math. Z.**25**(1926), no. 1, 388–404 (German). MR**1544819**, https://doi.org/10.1007/BF01283847**[17]**E. C. Titchmarsh,*Han-shu lun*, Translated from the English by Wu Chin, Science Press, Peking, 1964 (Chinese). MR**0197687****[18]**G. N. Watson,*A Treatise on the Theory of Bessel Functions*, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR**0010746**

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DOI:
https://doi.org/10.1090/S0002-9947-1969-0252330-1

Article copyright:
© Copyright 1969
American Mathematical Society