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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…
math.NT2006
Shifted and Shiftless Partition Identities II
Frank G. Garvan, Hamza Yesilyurt
Let S and T be sets of positive integers and let a be a fixed positive integer. An a-shifted partition identity has the form p(S,n)=p(T,n-a), for all n greater or equal to a. Here…
math.NT2006
New Identities for 7-cores with prescribed BG-rank
Alexander Berkovich, Hamza Yesilyurt
A q-series with nonnegative power series coefficients is called positive. The partition statistics BG-rank is defined as an alternating sum of parities of parts of a partition. It…