Zobrazeno 1 - 10
of 72
pro vyhledávání: '"Alan Adolphson"'
This two-volume book collects the lectures given during the three months cycle of lectures held in Northern Italy between May and July of 2001 to commemorate Professor Bernard Dwork (1923 - 1998). It presents a wide-ranging overview of some of the mo
Autor:
Alan Adolphson, Steven Sperber
Publikováno v:
Acta Arithmetica. 200:39-59
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3f80e3d44e7c3dcae420d23bb026f0ed
https://doi.org/10.4064/aa200427-5-4
https://doi.org/10.4064/aa200427-5-4
Autor:
Steven Sperber, Alan Adolphson
Publikováno v:
Finite Fields and Their Applications. 47:203-221
The Hasse–Witt matrix of a hypersurface in P n over a finite field of characteristic p gives essentially complete mod p information about the zeta function of the hypersurface. But if the degree d of the hypersurface is ≤n, the zeta function is t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e55b670869aea2d890bf1a466f88944d
https://doi.org/10.1016/j.ffa.2017.06.011
https://doi.org/10.1016/j.ffa.2017.06.011
Autor:
Alan Adolphson, Steven Sperber
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4c0a1ee87934613413b1ac4a5ea47d74
http://arxiv.org/abs/1911.10639
http://arxiv.org/abs/1911.10639
Autor:
Alan Adolphson, Steven Sperber
Publikováno v:
Finite Fields and Their Applications. 41:55-63
We give a short combinatorial proof of the generic invertibility of the Hasse–Witt matrix of a projective hypersurface. We also examine the relationship between the Hasse–Witt matrix and certain A-hypergeometric series, which is what motivated th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2c2f528bba59948f10fa9be8e8841464
https://doi.org/10.1016/j.ffa.2016.05.001
https://doi.org/10.1016/j.ffa.2016.05.001
Autor:
Alan Adolphson, Steven Sperber
Publikováno v:
Algebra Number Theory 11, no. 6 (2017), 1317-1356
By a "generalized Calabi-Yau hypersurface" we mean a hypersurface in ${\mathbb P}^n$ of degree $d$ dividing $n+1$. The zeta function of a generic such hypersurface has a reciprocal root distinguished by minimal $p$-divisibility. We study the $p$-adic
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fbc97392d3a20aa67bf7b59e1529132f
http://arxiv.org/abs/1602.03578
http://arxiv.org/abs/1602.03578
Autor:
Alan Adolphson, Steven Sperber
Publikováno v:
Proceedings of the American Mathematical Society. 140:2033-2042
In recent work, Beukers characterized A {A} -hypergeometric systems having a full set of algebraic solutions. He accomplished this by (1) determining which A {A} -hypergeometric systems have a full set of polynomial solutions modulo p p for almost al
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::fc95c8bb9c8b068d9438532240c74166
https://doi.org/10.1090/s0002-9939-2011-11073-6
https://doi.org/10.1090/s0002-9939-2011-11073-6
Autor:
Alan Adolphson, Steven Sperber
Publikováno v:
International Journal of Number Theory. :747-764
We find new conditions on a polynomial over a finite field that guarantee that the exponential sum defined by the polynomial has only one nonvanishing p-adic cohomology group, hence the L-function associated to the exponential sum is a polynomial or
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d6a35712a16b136318ed627195b9e13e
https://doi.org/10.1142/s1793042109002353
https://doi.org/10.1142/s1793042109002353
Autor:
Alan Adolphson, Steven Sperber
Publikováno v:
Journal of Algebra. 304:1193-1227
Let f_1,...,f_r be homogeneous polynomials in K[x_1,...,x_n], K a field. Put F=y_1f_1+...+y_rf_r in K[x,y] and let I be the ideal of K[x,y] generated by the partials of F relative to the x_i and y_j. The Jacobian ring of F is the quotient J:=K[x,y]/I
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b0ea4ed7bbd0a7c475189412ce6c3784
https://doi.org/10.1016/j.jalgebra.2006.06.039
https://doi.org/10.1016/j.jalgebra.2006.06.039
Autor:
Steven Sperber, Alan Adolphson
Publikováno v:
Transactions of the American Mathematical Society. 356:345-369
We prove a vanishing theorem for the p p -adic cohomology of exponential sums on A n \mathbf {A}^n . In particular, we obtain new classes of exponential sums on A n \mathbf {A}^n that have a single nonvanishing p p -adic cohomology group. The dimensi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3bd0a221aee698cfdaa42dbdf43e6eed
https://doi.org/10.1090/s0002-9947-03-03324-5
https://doi.org/10.1090/s0002-9947-03-03324-5