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math.NT2008
On the representations of integers by the sextenary quadratic form x^2+y^2+z^2+ 7s^2+7t^2+ 7u^2 and 7-cores
Alexander Berkovich, Hamza Yesilyurt
In this paper we derive an explicit formula for the number of representations of an integer by the sextenary form x^2+y^2+z^2+ 7s^2+7t^2+ 7u^2. We establish the following intriguin…
math.NT2006
Ramanujan's Identities and Representation of Integers by Certain Binary and Quaternary Quadratic Forms
Alexander Berkovich, Hamza Yesilyurt
We revisit old conjectures of Fermat and Euler regarding representation of integers by binary quadratic form x^2+5y^2. Making use of Ramanujan's_1ψ_1 summation formula we establish…