Zobrazeno 1 - 10
of 109
pro vyhledávání: '"Adolphson, Alan"'
Autor:
Adolphson, Alan, Sperber, Steven
We give a class of examples of $A$-hypergeometric systems that display integrality of mirror maps. Specifically, these systems have solutions $F(\lambda_1,\dots,\lambda_N) = 1$ and $\log\lambda^l + G(\lambda_1,\dots,\lambda_N)$ (for certain $l\in{\ma
Externí odkaz:
http://arxiv.org/abs/2410.04293
Autor:
Adolphson, Alan, Sperber, Steven
By a generalized Delsarte polynomial we mean a Laurent polynomial whose exponent vectors are linearly independent. We consider certain monomial deformations of generalized Delsarte polynomials and study their associated differential modules. We deter
Externí odkaz:
http://arxiv.org/abs/2312.01563
Autor:
Adolphson, Alan, Sperber, Steven
We describe the action of the Dwork-Frobenius operator on certain $A$-hypergeometric series. As a consequence, we obtain an integrality result for the coefficients of those series. This implies an integrality result for classical hypergeometric serie
Externí odkaz:
http://arxiv.org/abs/2204.09814
Autor:
Adolphson, Alan, Sperber, Steven
By a codimension-one system we mean a system whose lattice of relations has rank one. We consider codimension-one $A$-hypergeometric systems and explicitly construct some of the logarithmic series solutions at the origin. When the parameter vector $\
Externí odkaz:
http://arxiv.org/abs/2202.08389
Autor:
Adolphson, Alan, Sperber, Steven
We identify the $p$-adic unit roots of the zeta function of a projective hypersurface over a finite field of characteristic $p$ as the eigenvalues of a product of special values of a certain matrix of $p$-adic series. That matrix is a product $F(\Lam
Externí odkaz:
http://arxiv.org/abs/2001.07280
Autor:
Adolphson, Alan, Sperber, Steven
We use the Dwork-Frobenius operator to prove an integrality result for $A$-hypergeometric series whose coefficients are factorial ratios. As a special case, we generalize one direction of a classical result of Landau on the integrality of factorial r
Externí odkaz:
http://arxiv.org/abs/2001.03296
Autor:
Adolphson, Alan, Sperber, Steven
We return to some past studies of hyperkloosterman sums ([9,10]) via $p$-adic cohomology with an aim to improve earlier results. In particular, we work here with Dwork's $\theta_\infty$-splitting function and a better choice of basis for cohomology.
Externí odkaz:
http://arxiv.org/abs/1911.10639
Autor:
Adolphson, Alan, Sperber, Steven
Let $A$ be a set of $N$ vectors in ${\mathbb Z}^n$ and let $v$ be a vector in ${\mathbb C}^N$ that has minimal negative support for $A$. Such a vector $v$ gives rise to a formal series solution of the $A$-hypergeometric system with parameter $\beta=A
Externí odkaz:
http://arxiv.org/abs/1905.03235
Autor:
Adolphson, Alan, Sperber, Steven
Publikováno v:
In Journal of Number Theory February 2023 243:328-351
Autor:
Adolphson, Alan, Sperber, Steven
Let $X$ be the family of hypersurfaces in the odd-dimensional torus ${\mathbb T}^{2n+1}$ defined by a Laurent polynomial $f$ with fixed exponents and variable coefficients. We show that if $n\Delta$, the dilation of the Newton polytope $\Delta$ of $f
Externí odkaz:
http://arxiv.org/abs/1806.10243