6 papers
Mollified Moments of Cubic Dirichlet L-Functions over the Eisenstein Field
Ahmet M. Güloğlu, Hamza Yesilyurt
We prove, assuming the generalized Riemann Hypothesis (GRH) that there is a positive density of -functions associated with primitive cubic Dirichlet characters over the Eisenste…
On Rogers-Ramanujan functions, binary quadratic forms and eta-quotients
Alexander Berkovich, Hamza Yesilyurt
In a handwritten manuscript published with his lost notebook, Ramanujan stated without proofs forty identities for the Rogers-Ramanujan functions. We observe that the functions tha…
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…
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…
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…
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…