The Experts below are selected from a list of 26160 Experts worldwide ranked by ideXlab platform
Mark W Coffey - One of the best experts on this subject based on the ideXlab platform.
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ASYMPTOTIC ESTIMATION OF ξ(2n)(1/2) : ON A CONJECTURE OF FARMER AND RHOADES
Mathematics of Computation, 2008Co-Authors: Mark W CoffeyAbstract:We verify a very recent conjecture of Farmer and Rhoades on the asymptotic rate of growth of the derivatives of the Riemann Xi Function at s = 1/2. We give two separate proofs of this result, with the more general method not restricted to s = 1/2. We briefly describe other approaches to our results, give a heuristic argument, and mention supporting numerical evidence.
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New results concerning power series expansions of the Riemann Xi Function and the Li/Keiper constants
Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences, 2008Co-Authors: Mark W CoffeyAbstract:The Riemann hypothesis is equivalent to the Li criterion governing a sequence of real constants that are certain logarithmic derivatives of the Riemann Xi Function evaluated at unity. A new represe...
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theta and riemann Xi Function representations from harmonic oscillator eigensolutions
Physics Letters A, 2007Co-Authors: Mark W CoffeyAbstract:Abstract From eigensolutions of the harmonic oscillator or Kepler–Coulomb Hamiltonian we extend the Functional equation for the Riemann zeta Function and develop integral representations for the Riemann Xi Function that is the completed classical zeta Function. A key result provides a basis for generalizing the important Riemann–Siegel integral formula.
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Theta and Riemann Xi Function representations from harmonic oscillator eigensolutions
Physics Letters A, 2007Co-Authors: Mark W CoffeyAbstract:From eigensolutions of the harmonic oscillator or Kepler-Coulomb Hamiltonian we extend the Functional equation for the Riemann zeta Function and develop integral representations for the Riemann Xi Function that is the completed classical zeta Function. A key result provides a basis for generalizing the important Riemann-Siegel integral formula.Comment: 15 pages, no figures, appears in Phys. Lett.
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The theta-Laguerre calculus formulation of the Li/Keiper constants
Journal of Approximation Theory, 2007Co-Authors: Mark W CoffeyAbstract:The Riemann hypothesis is equivalent to the nonnegativity of a sequence of real constants {@l"k}"k"="1^~, that are certain logarithmic derivatives of the Riemann Xi Function evaluated at unity. We re-express these constants using the theta-Laguerre calculus. By using integral representations, we reformulate the coefficients {@l"k}"k"="1^~ together with a closely related sequence {a"j}"j"="0^~. We present a decomposition of the quantities a"j into superdominant and subdominant components and give an upper bound on the former and an asymptotic lower bound for the latter. Sufficient estimation of these quantities would lead to confirmation of the Riemann hypothesis.
Eric A. Flounders - One of the best experts on this subject based on the ideXlab platform.
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Factor Xia–specific IgG and a reversal agent to probe factor Xi Function in thrombosis and hemostasis
Science translational medicine, 2016Co-Authors: Tovo David, Yun Cheol Kim, Lauren Kate Ely, Isaac J. Rondon, Huilan Gao, Peter J. O'brien, Michael W. Bolt, Anthony J. Coyle, Jorge L. Garcia, Eric A. FloundersAbstract:Thrombosis is a major cause of morbidity and mortality. Current antithrombotic drugs are not ideal in that they must balance prevention of thrombosis against bleeding risk. Inhibition of coagulation factor Xi (FXi) may offer an improvement over eXisting antithrombotic strategies by preventing some forms of thrombosis with lower bleeding risk. To permit exploration of this hypothesis in humans, we generated and characterized a series of human immunoglobulin Gs (IgGs) that blocked FXia active-site Function but did not bind FXi zymogen or other coagulation proteases. The most potent of these IgGs, C24 and DEF, inhibited clotting in whole human blood and prevented FeCl 3 -induced carotid artery occlusion in FXi-deficient mice reconstituted with human FXi and in thread-induced venous thrombosis in rabbits at clinically relevant doses. At doses substantially higher than those required for inhibition of intravascular thrombus formation in these models, DEF did not increase cuticle bleeding in rabbits or cause spontaneous bleeding in macaques over a 2-week study. Anticipating the desirability of a reversal agent, we also generated a human IgG that rapidly reversed DEF activity ex vivo in human plasma and in vivo in rabbits. Thus, an active site–directed FXia-specific antibody can block thrombosis in animal models and, together with the reversal agent, may facilitate exploration of the roles of FXia in human disease.
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factor Xia specific igg and a reversal agent to probe factor Xi Function in thrombosis and hemostasis
Science Translational Medicine, 2016Co-Authors: Tovo David, Yun Cheol Kim, Lauren Kate Ely, Isaac J. Rondon, Huilan Gao, Michael W. Bolt, Anthony J. Coyle, Jorge L. Garcia, Peter J Obrien, Eric A. FloundersAbstract:Thrombosis is a major cause of morbidity and mortality. Current antithrombotic drugs are not ideal in that they must balance prevention of thrombosis against bleeding risk. Inhibition of coagulation factor Xi (FXi) may offer an improvement over eXisting antithrombotic strategies by preventing some forms of thrombosis with lower bleeding risk. To permit exploration of this hypothesis in humans, we generated and characterized a series of human immunoglobulin Gs (IgGs) that blocked FXia active-site Function but did not bind FXi zymogen or other coagulation proteases. The most potent of these IgGs, C24 and DEF, inhibited clotting in whole human blood and prevented FeCl 3 -induced carotid artery occlusion in FXi-deficient mice reconstituted with human FXi and in thread-induced venous thrombosis in rabbits at clinically relevant doses. At doses substantially higher than those required for inhibition of intravascular thrombus formation in these models, DEF did not increase cuticle bleeding in rabbits or cause spontaneous bleeding in macaques over a 2-week study. Anticipating the desirability of a reversal agent, we also generated a human IgG that rapidly reversed DEF activity ex vivo in human plasma and in vivo in rabbits. Thus, an active site–directed FXia-specific antibody can block thrombosis in animal models and, together with the reversal agent, may facilitate exploration of the roles of FXia in human disease.
Dmitry Ostrovsky - One of the best experts on this subject based on the ideXlab platform.
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A Note on the $S_2(\delta)$ Distribution and the Riemann Xi Function
Electronic Communications in Probability, 2014Co-Authors: Dmitry OstrovskyAbstract:The theory of $S_2(\delta)$ family of probability distributions is used to give a derivation of the Functional equation of the Riemann Xi Function. The $\delta$ deformation of the Xi Function is formulated in terms of the $S_2(\delta)$ distribution and shown to satisfy Riemann's Functional equation. Criteria for simplicity of roots of the Xi Function and for its simple roots to satisfy the Riemann hypothesis are formulated in terms of a differentiability property of the $S_2(\delta)$ family. For application, the values of the Riemann zeta Function at the integers and of the Riemann Xi Function in the complex plane are represented as integrals involving the Laplace transform of $S_2.$
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a note on the s_2 delta distribution and the riemann Xi Function
Electronic Communications in Probability, 2014Co-Authors: Dmitry OstrovskyAbstract:The theory of $S_2(\delta)$ family of probability distributions is used to give a derivation of the Functional equation of the Riemann Xi Function. The $\delta$ deformation of the Xi Function is formulated in terms of the $S_2(\delta)$ distribution and shown to satisfy Riemann's Functional equation. Criteria for simplicity of roots of the Xi Function and for its simple roots to satisfy the Riemann hypothesis are formulated in terms of a differentiability property of the $S_2(\delta)$ family. For application, the values of the Riemann zeta Function at the integers and of the Riemann Xi Function in the complex plane are represented as integrals involving the Laplace transform of $S_2.$
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On Barnes beta distributions, Selberg integral and Riemann Xi
Forum Mathematicum, 2014Co-Authors: Dmitry OstrovskyAbstract:AbstractThe theory of Barnes beta probability distributions is advanced and related to the Riemann Xi Function. The scaling invariance, multiplication formula, and Shintani factorization of Barnes multiple gamma Functions are reviewed using the approach of Ruijsenaars and shown to imply novel properties of Barnes beta distributions. The applications are given to the meromorphic extension of the Selberg integral as a Function of its dimension and the scaling invariance of the underlying probability distribution. This probability distribution in the critical case is described and conjectured to be the distribution of the derivative martingale. The Jacobi triple product is interpreted probabilistically resulting in an approXimation of the Riemann Xi Function by the Mellin transform of the logarithm of a limit of Barnes beta distributions.
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A note on the S2( ) distribution and the Riemann Xi Function
2014Co-Authors: Dmitry OstrovskyAbstract:The theory ofS2( ) family of probability distributions is used to give a derivation of the Functional equation of the Riemann Xi Function. The deformation of the Xi Function is formulated in terms of theS2( ) distribution and shown to satisfy Riemann’s Functional equation. Criteria for simplicity of roots of the Xi Function and for its simple roots to satisfy the Riemann hypothesis are formulated in terms of a differentiability property of the S2( ) family. For application, the values of the Riemann zeta Function at the integers and of the Riemann Xi Function in the complex plane are represented as integrals involving the Laplace transform of S2:
Atul Dixit - One of the best experts on this subject based on the ideXlab platform.
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zeros of combinations of the riemann Xi Function and the confluent hypergeometric Function on bounded vertical shifts
arXiv: Number Theory, 2017Co-Authors: Atul Dixit, Rahul Kumar, Bibekananda Maji, Alexandru ZaharescuAbstract:In 1914, Hardy proved that infinitely many non-trivial zeros of the Riemann zeta Function lie on the critical line using the transformation formula of the Jacobi theta Function. Recently the first author obtained an integral representation involving the Riemann $\Xi$-Function and the confluent hypergeometric Function linked to the general theta transformation. Using this result, we show that a series consisting of bounded vertical shifts of a product of the Riemann $\Xi$-Function and the real part of a confluent hypergeometric Function has infinitely many zeros on the critical line, thereby generalizing a previous result due to the first and the last authors along with Roy and Robles. The latter itself is a generalization of Hardy's theorem.
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Analogues of the general theta transformation formula
arXiv: Number Theory, 2011Co-Authors: Atul DixitAbstract:A new class of integrals involving the confluent hypergeometric Function ${}_1F_{1}(a;c;z)$ and the Riemann $\Xi$-Function is considered. It generalizes a class containing some integrals of S. Ramanujan, G.H. Hardy and W.L. Ferrar and gives as by-products, transformation formulas of the form $F(z,\alpha)=F(iz,\beta)$, where $\alpha\beta=1$. As particular examples, we derive an extended version of the general theta transformation formula and generalizations of certain formulas of Ferrar and Hardy. A one-variable generalization of a well-known identity of Ramanujan is also given. We conclude with a generalization of a conjecture due to Ramanujan, Hardy and J.E. Littlewood involving infinite series of M\"obius Functions.
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Character analogues of Ramanujan type integrals involving the Riemann $\Xi$-Function
arXiv: Number Theory, 2011Co-Authors: Atul DixitAbstract:A new class of integrals involving the product of $\Xi$-Functions associated with primitive Dirichlet characters is considered. These integrals give rise to transformation formulas of the type $F(z, \alpha,\chi)=F(-z, \beta,\bar{\chi})=F(-z,\alpha,\bar{\chi})=F(z,\beta,\chi)$, where $\alpha\beta=1$. New character analogues of transformation formulas of Guinand and Koshliakov as well as those of a formula of Ramanujan and its recent generalization are shown as particular examples. Finally, character analogues of a conjecture of Ramanujan, Hardy and Littlewood involving infinite series of M\"{o}bius Functions are derived.
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character analogues of ramanujan type integrals involving the riemann Xi Function
arXiv: Number Theory, 2011Co-Authors: Atul DixitAbstract:A new class of integrals involving the product of $\Xi$-Functions associated with primitive Dirichlet characters is considered. These integrals give rise to transformation formulas of the type $F(z, \alpha,\chi)=F(-z, \beta,\bar{\chi})=F(-z,\alpha,\bar{\chi})=F(z,\beta,\chi)$, where $\alpha\beta=1$. New character analogues of transformation formulas of Guinand and Koshliakov as well as those of a formula of Ramanujan and its recent generalization are shown as particular examples. Finally, character analogues of a conjecture of Ramanujan, Hardy and Littlewood involving infinite series of M\"{o}bius Functions are derived.
Tovo David - One of the best experts on this subject based on the ideXlab platform.
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Factor Xia–specific IgG and a reversal agent to probe factor Xi Function in thrombosis and hemostasis
Science translational medicine, 2016Co-Authors: Tovo David, Yun Cheol Kim, Lauren Kate Ely, Isaac J. Rondon, Huilan Gao, Peter J. O'brien, Michael W. Bolt, Anthony J. Coyle, Jorge L. Garcia, Eric A. FloundersAbstract:Thrombosis is a major cause of morbidity and mortality. Current antithrombotic drugs are not ideal in that they must balance prevention of thrombosis against bleeding risk. Inhibition of coagulation factor Xi (FXi) may offer an improvement over eXisting antithrombotic strategies by preventing some forms of thrombosis with lower bleeding risk. To permit exploration of this hypothesis in humans, we generated and characterized a series of human immunoglobulin Gs (IgGs) that blocked FXia active-site Function but did not bind FXi zymogen or other coagulation proteases. The most potent of these IgGs, C24 and DEF, inhibited clotting in whole human blood and prevented FeCl 3 -induced carotid artery occlusion in FXi-deficient mice reconstituted with human FXi and in thread-induced venous thrombosis in rabbits at clinically relevant doses. At doses substantially higher than those required for inhibition of intravascular thrombus formation in these models, DEF did not increase cuticle bleeding in rabbits or cause spontaneous bleeding in macaques over a 2-week study. Anticipating the desirability of a reversal agent, we also generated a human IgG that rapidly reversed DEF activity ex vivo in human plasma and in vivo in rabbits. Thus, an active site–directed FXia-specific antibody can block thrombosis in animal models and, together with the reversal agent, may facilitate exploration of the roles of FXia in human disease.
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factor Xia specific igg and a reversal agent to probe factor Xi Function in thrombosis and hemostasis
Science Translational Medicine, 2016Co-Authors: Tovo David, Yun Cheol Kim, Lauren Kate Ely, Isaac J. Rondon, Huilan Gao, Michael W. Bolt, Anthony J. Coyle, Jorge L. Garcia, Peter J Obrien, Eric A. FloundersAbstract:Thrombosis is a major cause of morbidity and mortality. Current antithrombotic drugs are not ideal in that they must balance prevention of thrombosis against bleeding risk. Inhibition of coagulation factor Xi (FXi) may offer an improvement over eXisting antithrombotic strategies by preventing some forms of thrombosis with lower bleeding risk. To permit exploration of this hypothesis in humans, we generated and characterized a series of human immunoglobulin Gs (IgGs) that blocked FXia active-site Function but did not bind FXi zymogen or other coagulation proteases. The most potent of these IgGs, C24 and DEF, inhibited clotting in whole human blood and prevented FeCl 3 -induced carotid artery occlusion in FXi-deficient mice reconstituted with human FXi and in thread-induced venous thrombosis in rabbits at clinically relevant doses. At doses substantially higher than those required for inhibition of intravascular thrombus formation in these models, DEF did not increase cuticle bleeding in rabbits or cause spontaneous bleeding in macaques over a 2-week study. Anticipating the desirability of a reversal agent, we also generated a human IgG that rapidly reversed DEF activity ex vivo in human plasma and in vivo in rabbits. Thus, an active site–directed FXia-specific antibody can block thrombosis in animal models and, together with the reversal agent, may facilitate exploration of the roles of FXia in human disease.
