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Lines Full of Dedekind Sums

open access: yes, 2004
G. Myerso, N. Phillips
semanticscholar   +1 more source
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Further two dimensional series evaluations via the elliptic functions of Ramanujan and Jacobi

, 2014
Recently, B. C. Berndt, G. Lamb and M. Rogers [4] have shown that it is possible to evaluate F(a,b)(x) := ∞ ∑ n=−∞ ∞ ∑ m=−∞ (−1)m+n (xm)2 + (an+ b)2 for any positive rational value of x and for many values of (a, b) ∈ N2.
K. R. Vasuki, R. G. Veeresha, K. Alloush
semanticscholar   +1 more source

A Hybrid Mean Value Involving the Dedekind Sums and Exponential Sums

, 2014
In this paper, we use the analytic method and the properties of Gauss sums to study the hybrid mean value problem involving the classical Dedekind sums and exponential sums, and give several interesting identities and asymptotic formulae for it. Keywords:
Li Jianghua, Zhang Wenpeng
semanticscholar   +1 more source

Two Identities of Ramanujan’s Cubic Continued Fraction by Modular Equations

, 2013
In this paper, we establish two identities providing the relations between Ramanujan’s cubic continued fraction G(q) := q1/3 1 + q + q2 1 + q2 + q4 1 +... , |q| < 1 and two continued fractions G(q11) and G(q13).
B. R. S. Kumar, T. G. Sreeramamurthy
semanticscholar   +1 more source

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