Search Results - "Farmer, David W."

A new generation of mathematics textbook research and development by O’Halloran, Kay L., Beezer, Robert A., Farmer, David W.

“…This paper adopts a multimodal approach to the latest generation of digital mathematics textbooks (print and online) to investigate how the design, content,…”
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Differentiation evens out zero spacings by Farmer, David W., Rhoades, Robert C.

“…If f is a polynomial with all of its roots on the real line, then the roots of the derivative f' are more evenly spaced than the roots of f. The same holds for…”
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Analytic L-functions: Definitions, theorems, and connections by Farmer, David W., Pitale, Ameya, Ryan, Nathan C., Schmidt, Ralf

“…L-functions can be viewed axiomatically, such as in the formulation due to Selberg, or they can be seen as arising from cuspidal automorphic representations of…”
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Palindromic random trigonometric polynomials by Conrey, J. Brian, Farmer, David W., Imamoglu, Özlem

“…We show that if a real trigonometric polynomial has few real roots, then the trigonometric polynomial obtained by writing the coefficients in reverse order…”
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The second Dirichlet coefficient starts out negative by Farmer, David W., Koutsoliotas, Sally

“…Classical modular forms of small weight and low level are likely to have a negative second Fourier coefficient. Similarly, the labeling scheme for elliptic…”
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Pair correlation of the zeros of the derivative of the Riemann ξ‐function by Farmer, David W., Gonek, Steven M., Lee, Yoonbok

“…The complex zeros of the Riemannn zeta‐function are identical to the zeros of the Riemann ξ‐function, ξ(s). Thus, if the Riemann hypothesis (RH) is true for…”
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SURVEY ARTICLE: CHARACTERIZATIONS OF THE SAITO-KUROKAWA LIFTING by FARMER, DAVID W., PITALE, AMEYA, RYAN, NATHAN C., SCHMIDT, RALF

“…There are a variety of characterizations of Saito-Kurokawa lifts from elliptic modular forms to Siegel modular forms of degree 2. In addition to giving a…”
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Jensen polynomials are not a plausible route to proving the Riemann Hypothesis by Farmer, David W.

“…Recent work on the Jensen polynomials of the Riemann xi-function and its derivatives found a connection to the Hermite polynomials. Those results have been…”
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Crystallization of random trigonometric polynomials by FARMER, David W, YERRINGTON, Mark

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TESTING THE FUNCTIONAL EQUATION OF A HIGH-DEGREE EULER PRODUCT by FARMER, David W, RYAN, Nathan C, SCHMIDT, Ralf

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The Nontrivial Zeros of Period Polynomials of Modular Forms Lie on the Unit Circle by Conrey, John Brian, Farmer, David W., Imamoglu, Özlem

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Maass Forms on GL(3) and GL(4) by Farmer, David W., Koutsoliotas, Sally, Lemurell, Stefan

“…We describe a practical method for finding an L-function without first finding an associated underlying object. The procedure involves using the Euler product,…”
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Currently there are no reasons to doubt the Riemann Hypothesis by Farmer, David W

“…We examine published arguments which suggest that the Riemann Hypothesis may not be true. In each case we provide evidence to explain why the claimed argument…”
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Landau–Siegel zeros and zeros of the derivative of the Riemann zeta function by Farmer, David W., Ki, Haseo

“…We show that if the derivative of the Riemann zeta function has sufficiently many zeros close to the critical line, then the zeta function has many closely…”
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When are the roots of a polynomial real and distinct? A graphical view by Farmer, David W

“…We prove the classical result, which goes back at least to Fourier, that a polynomial with real coefficients has all zeros real and distinct if and only if the…”
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Jensen polynomials are not a plausible route to proving the Riemann Hypothesis by Farmer, David W

“…Recent work on the Jensen polynomials of the Riemann xi-function and its derivatives found a connection to the Hermite polynomials. Those results have been…”
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The highest lowest zero of general L-functions by Bober, Jonathan, Conrey, J. Brian, Farmer, David W., Fujii, Akio, Koutsoliotas, Sally, Lemurell, Stefan, Rubinstein, Michael, Yoshida, Hiroyuki

“…Stephen D. Miller showed that, assuming the Generalized Riemann Hypothesis, every entire L-function of real archimedean type has a zero in the interval 12+it…”
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Converse theorems assuming a partial euler product by Farmer, David W., Wilson, Kevin

“…Associated to a newform f ( z ) is a Dirichlet series L f ( s ) with functional equation and Euler product. Hecke showed that if the Dirichlet series F ( s )…”
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The Landscape of L-functions: degree 3 and conductor 1 by Farmer, David W, Koutsoliotas, Sally, Lemurell, Stefan, Roberts, David P

“…We extend previous lists by numerically computing approximations to many L-functions of degree $d=3$, conductor $N=1$, and small spectral parameters. We sketch…”
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The Power of Symmetry by Farmer, David W.

“…By the 18th century, mathematics and mathematical notation had matured to the point of finding explicit formulas for the roots of general polynomials of degree…”
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