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Hypergeometric evaluation identities and supercongruences
We apply some hypergeometric evaluation identities, including a strange valuation of Gosper, to prove several supercongruences related to special valuations of truncated hypergeometric series. InExpand
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Some supercongruences occurring in truncated hypergeometric series
For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of $p$-adic Gamma functions that are stronger than those one can expect toExpand
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Resilience and social support promote posttraumatic growth of women with infertility: The mediating role of positive coping
According to previous research, clinical experience with individuals facing infertility has demonstrated that positive psychological changes can arise from the struggle involved (Paul et al., 2010),Expand
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Hypergeometric Functions over Finite Fields
We discuss recent work of the authors in which we study the translation of classical hypergeometric transformation and evaluation formulas to the finite field setting.
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On Atkin–Swinnerton-Dyer congruence relations
Abstract In this paper, we exhibit a noncongruence subgroup Γ whose space of weight 3 cusp forms S 3 ( Γ ) admits a basis satisfying the Atkin–Swinnerton-Dyer congruence relations with two weight 3Expand
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Supercongruences and Complex Multiplication
We study congruences involving truncated hypergeometric series of the form_rF_{r-1}(1/2,...,1/2;1,...,1;\lambda)_{(mp^s-1)/2} = \sum_{k=0}^{(mp^s-1)/2} ((1/2)_k/k!)^r \lambda^k where p is a prime andExpand
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MODULAR FORMS FOR NONCONGRUENCE SUBGROUPS
(Z) has been oneof the central topics in number theory for over one century. It has broad applica-tions and impact to many branches of mathematics. Langlands’ program is a vastgeneralization of thisExpand
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On modular forms for some noncongruence subgroups of SL2(Z)
In this paper, we consider modular forms for finite index subgroups of the modular group whose Fourier coefficients are algebraic. It is well known that the Fourier coefficients of any holomorphicExpand
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Knockdown of FoxO3a induces increased neuronal apoptosis during embryonic development in zebrafish
Neuronal apoptosis sculpts the developing brain, and nearly all identified classes of neurons seem to be produced "in excess" during development. FoxO transcription factors regulate apoptosis inExpand
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