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http://dx.doi.org/10.4134/BKMS.b150870

A FAMILY OF FUNCTIONS ASSOCIATED WITH THREE TERM RELATIONS AND EISENSTEIN SERIES  

Aygunes, Aykut Ahmet (Department of Mathematics Akdeniz University)
Publication Information
Bulletin of the Korean Mathematical Society / v.53, no.6, 2016 , pp. 1671-1683 More about this Journal
Abstract
Abstract. In this paper, for $a{\in}C$, we investigate functions $g_a$ and ${\psi}_a$ associated with three term relations. $g_a$ is defined by means of function ${\psi}_a$. By using these functions, we obtain some functional equations related to the Eisenstein series and the Riemann zeta function. Also we find a generalized difference formula of function $g_a$.
Keywords
three term relations; period function; Eisenstein series; Riemann zeta function;
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1 R. Bruggeman, Automorphic forms, hyperfunction cohomology, and period functions, J. Reine Angew. Math. 492 (1997), 1-39.
2 A. Ivic, The Riemann Zeta Function, John Wiley & Sons, 1985.
3 J. B. Lewis, Spaces of holomorphic functions equivalent to the even Maass cusp forms, Invent. Math. 127 (1997), no. 2, 271-306.   DOI
4 J. B. Lewis and D. Zagier, Period functions and the Selberg zeta function for the modular group, The mathematical beauty of physics (Saclay, 1996), 83-97, Adv. Ser. Math. Phys., 24, World Sci. Publ., River Edge, NJ, 1997.
5 M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Applied Mathematics Series 55, 1972.
6 T. M. Apostol, Modular functions and Dirichlet Series in Number Theory, Berlin, Heidelberg, and New York, Springer-Verlag, 1976.
7 T. M. Apostol, Introduction to Analytic Number Theory, Berlin, Heidelberg, and New York, Springer-Verlag, 1976.
8 S. Bettin and B. Conrey, Period functions and cotangent sums, Algebra Number Theory 7 (2013), no. 1, 215-242.   DOI
9 Y. Simsek, On Weierstrass ${\wp}$(z)-function, Hardy sums and Eisenstein series, Proc. Jangjeon Math. Soc. 7 (2004), no. 2, 99-108.
10 Y. Simsek, Relations between theta-functions, Hardy sums, Eisenstein series and Lambert series in the transformation formula of log ${\eta}_{1,h}$(z), J. Number Theory 99 (2003), no. 2, 338-360.   DOI
11 H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, 2001.
12 J. B. Lewis and D. Zagier, Period functions for Maass wave forms. I, Ann. of Math. (2) 153 (2001), no. 1, 191-258.   DOI