Zobrazeno 1 - 10
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pro vyhledávání: '"Rogers, Mathew"'
Autor:
Rogers, Mathew D.
The logarithmic Mahler measure of an n-variable Laurent polynomial, P(x1,...,xn) is defined by [expression]. Using experimental methods, David Boyd conjectured a large number of explicit relations between Mahler measures of polynomials and special va
Externí odkaz:
http://hdl.handle.net/2429/1420
Publikováno v:
Math. Z. 276 (2014), no. 3-4, 1151-1163
The aim of this paper is to prove a Mahler measure formula of a four-variable Laurent polynomial whose zero locus defines a Calabi-Yau threefold. We show that its Mahler measure is a rational linear combination of a special L-value of the normalized
Externí odkaz:
http://arxiv.org/abs/1305.2143
We study the series $\psi_s(z):=\sum_{n=1}^{\infty} \sec(n\pi z)n^{-s}$, and prove that it converges under mild restrictions on $z$ and $s$. The function possesses a modular transformation property, which allows us to evaluate $\psi_{s}(z)$ explicitl
Externí odkaz:
http://arxiv.org/abs/1304.3922
Autor:
Rogers, Mathew, Straub, Armin
We prove a Ramanujan-type formula for $520/\pi$ conjectured by Sun. Our proof begins with a hypergeometric representation of the relevant double series, which relies on a recent generating function for Legendre polynomials by Wan and Zudilin. After s
Externí odkaz:
http://arxiv.org/abs/1210.2373
Autor:
Rogers, Mathew
We prove formulas for special values of the Ramanujan tau zeta function. Our formulas show that $L(\Delta, k)$ is a period in the sense of Kontsevich and Zagier when $k\ge12$. As an illustration, we reduce $L(\Delta, k)$ to explicit integrals of hype
Externí odkaz:
http://arxiv.org/abs/1210.1942
We show that the integral $J(t) = (1/\pi^3) \int_0^\pi \int_0^\pi \int_0^\pi dx dy dz \log(t - \cos{x} - \cos{y} - \cos{z} + \cos{x}\cos{y}\cos{z})$, can be expressed in terms of ${_5F_4}$ hypergeometric functions. The integral arises in the solution
Externí odkaz:
http://arxiv.org/abs/1208.3345
We define the notion of a spanning tree generating function (STGF) $\sum a_n z^n$, which gives the spanning tree constant when evaluated at $z=1,$ and gives the lattice Green function (LGF) when differentiated. By making use of known results for loga
Externí odkaz:
http://arxiv.org/abs/1207.2815
Autor:
Guillera, Jesús, Rogers, Mathew
Publikováno v:
J. Aust. Math. Soc. 97 (2014) 78-106
We prove that there is a correspondence between Ramanujan-type formulas for 1/\pi, and formulas for Dirichlet L-values. The same method also allows us to resolve certain values of the Epstein zeta function in terms of rapidly converging hypergeometri
Externí odkaz:
http://arxiv.org/abs/1206.3981
We evaluate in closed form, for the first time, certain classes of double series, which are remindful of lattice sums. Elliptic functions, singular moduli, class invariants, and the Rogers--Ramanujan continued fraction play central roles in our evalu
Externí odkaz:
http://arxiv.org/abs/1108.4980
Autor:
Lalin, Matilde, Rogers, Mathew
We observe that five polynomial families have all of their zeros on the unit circle. We prove the statements explicitly for four of the polynomial families. The polynomials have coefficients which involve Bernoulli numbers, Euler numbers, and the odd
Externí odkaz:
http://arxiv.org/abs/1106.1189