Results 51 to 60 of about 563,274 (244)
GOLDFELD’S CONJECTURE AND CONGRUENCES BETWEEN HEEGNER POINTS
Forum of Mathematics, Sigma, 2019 Given an elliptic curve $E$ over $\mathbb{Q}$, a celebrated conjecture of Goldfeld asserts that a positive proportion of its quadratic twists should have analytic rank 0 (respectively 1).
DANIEL KRIZ, CHAO LI
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International Journal of Mathematics and Mathematical Sciences, 2020 We propose reduced Collatz conjecture and prove that it is equivalent to Collatz conjecture but more primitive due to reduced dynamics. We study reduced dynamics (that consists of occurred computations from any starting integer to the first integer less ...
Wei Ren
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Modular factorization of superconformal indices
Journal of High Energy Physics, 2023 Superconformal indices of four-dimensional N $$ \mathcal{N} $$ = 1 gauge theories factorize into holomorphic blocks. We interpret this as a modular property resulting from the combined action of an SL(3, ℤ) and SL(2, ℤ) ⋉ ℤ 2 transformation.
Vishnu Jejjala +3 more
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Short-Interval Averages of Sums of Fourier Coefficients of Cusp Forms
, 2016 Let $f$ be a weight $k$ holomorphic cusp form of level one, and let $S_f(n)$ denote the sum of the first $n$ Fourier coefficients of $f$. In analogy with Dirichlet's divisor problem, it is conjectured that $S_f(X) \ll X^{\frac{k-1}{2} + \frac{1}{4 ...
Hulse, Thomas A. +3 more
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Pediatric Blood &Cancer, EarlyView.ABSTRACT Background While Wilms tumor (WT) typically has a favorable prognosis, relapsed cases—especially those with high‐risk histology—remain therapeutically challenging after intensive frontline therapy. The combination of vincristine and irinotecan has demonstrated activity in pediatric solid tumors, and pazopanib, a multi‐targeted tyrosine kinase ...
Maria Debora De Pasquale +6 more
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Pediatric Blood &Cancer, EarlyView.ABSTRACT We sought to identify potential early risk biomarkers for lung disease in children post‐allogeneic HCT. Patients with pulmonary function tests 3 months post‐transplant and plasma samples between days 7 and 14 post‐HCT were included. Six of 27 subjects enrolled had reduced forced expiratory volume 1 (FEV1) z scores.
Isabella S. Small +3 more
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A New Approach on Proving Collatz Conjecture
Journal of Mathematics, 2019 Collatz Conjecture (3x+1 problem) states any natural number x will return to 1 after 3⁎x+1 computation (when x is odd) and x/2 computation (when x is even). In this paper, we propose a new approach for possibly proving Collatz Conjecture (CC). We propose
Wei Ren
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Surpassing the Ratios Conjecture in the 1-level density of Dirichlet $L$-functions
, 2014 We study the $1$-level density of low-lying zeros of Dirichlet $L$-functions in the family of all characters modulo $q$, with $Q/2 < q\leq Q$. For test functions whose Fourier transform is supported in $(-3/2, 3/2)$, we calculate this quantity beyond the
Conrey +9 more
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Pediatric Blood &Cancer, EarlyView.ABSTRACT The pediatric hematology‐oncology fellowship training curriculum has not substantially changed since its inception. The first year of training is clinically focused, and the second and third years are devoted to scholarship. However, this current structure leaves many fellows less competitive in the current job market, resulting in ...
Scott C. Borinstein +3 more
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On {a, b}-Edge-Weightings of Bipartite Graphs with Odd a, b
Discussiones Mathematicae Graph Theory, 2022 For any S ⊂ ℤ we say that a graph G has the S-property if there exists an S-edge-weighting w : E(G) → S such that for any pair of adjacent vertices u, v we have ∑e∈E(v) w(e) ≠ ∑e∈E(u) w(e), where E(v) and E(u) are the sets of edges incident to v and u ...
Bensmail Julien +2 more
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