Browsing by Author "Yeşilyurt, Hamza"

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    A generalization of a modular identity of Rogers
    (Academic Press, 2009) Yeşilyurt, Hamza
    In a handwritten manuscript published with his lost notebook, Ramanujan stated without proofs forty identities for the Rogers-Ramanujan functions. Most of the elementary proofs given for these identities are based on Schröter-type theta function identities in particular, the identities of L.J. Rogers. We give a generalization of Rogers's identity that also generalizes similar formulas of H. Schröter, and of R. Blecksmith, J. Brillhart, and I. Gerst. Applications to modular equations, Ramanujan's identities for the Rogers-Ramanujan functions as well as new identities for these functions are given.
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    Mollified moments of cubic Dirichlet L-functions over the Eisenstein field
    (Elsevier, 2023-12-10) Güloǧlu, Ahmet Muhtar; Yeşilyurt, Hamza
    We prove, assuming the generalized Riemann Hypothesis (GRH) that there is a positive density of L-functions associated with primitive cubic Dirichlet characters over the Eisenstein field that do not vanish at the central point. This is achieved by computing the first mollified moment, which is obtained unconditionally, and finding a sharp upper bound for the higher mollified moments for these L-functions, under GRH. The proportion of non-vanishing is explicit, but extremely small.
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    Ramanujan's circular summation, t-cores and twisted partition identities
    (Elsevier, 2019) Berkovich, A.; Garvan, F.; Yeşilyurt, Hamza
    In this paper, we give new evaluations for Ramanujan’s circular summation function. We also provide simpler proofs for known evaluations and give some generalizations. We discover modular relations among circular summation function partition function and give uniform proof of Ramanujan’s partition congruences for the moduli 5, 7 and 11. We also prove several interesting congruence relations.