Results 11 to 20 of about 236 (50)
Some theorems on the explicit evaluation of Ramanujan′s theta‐functions
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 40, Page 2149-2159, 2004., 2004 Bruce C. Berndt et al. and Soon‐Yi Kang have proved many of Ramanujan′s formulas for the explicit evaluation of the Rogers‐Ramanujan continued fraction and theta‐functions in terms of Weber‐Ramanujan class invariants. In this note, we give alternative proofs of some of these identities of theta‐functions recorded by Ramanujan in his notebooks and ...
Nayandeep Deka Baruah, P. Bhattacharyya
wiley +1 more source
The hybrid mean value of Dedekind sums and two-term exponential sums
Open Mathematics, 2016 In this paper, we use the mean value theorem of Dirichlet L-functions, the properties of Gauss sums and Dedekind sums to study the hybrid mean value problem involving Dedekind sums and the two-term exponential sums, and give an interesting identity and ...
Leran Chang, Xiaoxue Li
doaj +1 more source
On the mean value of the two-term Dedekind sums
Journal of Inequalities and Applications, 2013 The main purpose of this paper is, using the properties of Gauss sums, the estimate for character sums and the analytic method, to study the mean value of the two-term Dedekind sums and give an interesting asymptotic formula for it. MSC:11F20, 11L40.
Kang Xiaoyu, Wu Zhengang
semanticscholar +2 more sources
On the Mahler measure of hyperelliptic families
, 2016 We prove Boyd's "unexpected coincidence" of the Mahler measures for two families of two-variate polynomials defining curves of genus 2. We further equate the same measures to the Mahler measures of polynomials $y^3-y+x^3-x+kxy$ whose zero loci define ...
Bertin, Marie José, Zudilin, Wadim
core +2 more sources
Arithmetic of generalized Dedekind sums and their modularity
Open Mathematics, 2018 Dedekind sums were introduced by Dedekind to study the transformation properties of Dedekind η function under the action of SL2(ℤ). In this paper, we study properties of generalized Dedekind sums si,j(p, q). We prove an asymptotic expansion of a function
Choi Dohoon +3 more
doaj +1 more source
K. Saito's Conjecture for Nonnegative Eta Products and Analogous Results for Other Infinite Products [PDF]
, 2007 We prove that the Fourier coefficients of a certain general eta product considered by K. Saito are nonnegative. The proof is elementary and depends on a multidimensional theta function identity. The z=1 case is an identity for the generating function for
Berkovich, Alexander, Garvan, Frank G.
core +2 more sources
Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52
Open Mathematics, 2017 The convolution sum, ∑(l,m)∈N02αl+βm=nσ(l)σ(m), $ \begin{array}{} \sum\limits_{{(l\, ,m)\in \mathbb{N}_{0}^{2}}\atop{\alpha \,l+\beta\, m=n}} \sigma(l)\sigma(m), \end{array} $ where αβ = 22, 44, 52, is evaluated for all natural numbers n. Modular forms
Ntienjem Ebénézer
doaj +1 more source
Evaluation of the convolution sums ∑al+bm=n lσ(l) σ(m) with ab ≤ 9
Open Mathematics, 2017 The generating functions of divisor functions are quasimodular forms of weight 2 and their products belong to a space of quasimodular forms of higher weight.
Park Yoon Kyung
doaj +1 more source
Some special finite sums related to the three-term polynomial relations and their applications
Advances in Differential Equations, 2014 We define some finite sums which are associated with the Dedekind type sums and Hardy-Berndt type sums. The aim of this paper is to prove a reciprocity law for one of these sums. Therefore, we define a new function which is related to partial derivatives
Elif Çeti̇n, Y. Simsek, I. N. Cangul
semanticscholar +2 more sources
When are two Dedekind sums equal?
, 2011 A natural question about Dedekind sums is to find conditions on the integers $a_1, a_2$, and $b$ such that $s(a_1,b) = s(a_2, b)$. We prove that if the former equality holds then $ b \ | \ (a_1a_2-1)(a_1-a_2)$.
Jabuka, Stanislav +2 more
core +1 more source