2 edition of **On the zeta function of a hypersurface** found in the catalog.

On the zeta function of a hypersurface

Bernard M. Dwork

- 292 Want to read
- 17 Currently reading

Published
**1962**
by Institut des hautes études scientifiques in Paris
.

Written in English

- Functions, Zeta.,
- Surfaces.,
- Hyperspace.,
- Banach spaces.

**Edition Notes**

Other titles | Numérisation de documents anciens mathématiques (Online database), Endomorphismes complément continus des espaces de Banach p-adiques. |

Statement | by Bernard Dwork. Endomorphismes complément continus des espaces de Banach p-adiques, par Jean-Pierre Serre. |

Series | Institut des hautes études scientifiques (Paris, France) Publications mathématiques -- no. 12, Publications mathématiques (Institut des hautes études scientifiques (Paris, France)) -- no. 12. |

Contributions | Serre, Jean Pierre. |

The Physical Object | |
---|---|

Pagination | 85 p. |

Number of Pages | 85 |

ID Numbers | |

Open Library | OL13589598M |

In mathematics, the Dirac delta function (δ function) is a generalized function or distribution introduced by the physicist Paul is used to model the density of an idealized point mass or point charge as a function equal to zero everywhere except for zero and whose integral over the entire real line is equal to one. As there is no function that has these properties, the computations. The function zeta uses pts to compute the L-polynomial of X using the point counts computed by the provided function TracesToLPolynomial to convert the list of integers p +1 #X(Fpr) for 1 r g to the corresponding L-polynomial. Once you have implemented your function, test it on the provided polynomials f3 and f4 at small good primes p >1+e=r (you can compare your results with the.

Abstract. In this paper, we study the relation between the zeta function of a Calabi-Yau hypersurface and the zeta function of its mirror. Two types of arithmetic relations are discovered. This motivates us to formulate two general arithmetic mirror conjectures for the Author: Daqing Wan. the monodromy operator of an isolated hypersurface or complete intersection singularity. The investigation of this operator started in with the proof of the famous monodromy theorem (see §1). This theorem can be proved Mathematics Subject Classiﬁcation. 14D05, 32S40 Key words. monodromy, zeta function, spectrum, isolated singularity.

Congruent zeta function. Sperber and Voight, "Computing zeta functions of nondegenerate hypersurfaces with few monomials" Chiu Fai Wong, "Zeta Functions of Projective Toric Hypersurfaces over Finite Fields" Despite the name, this really just does zeta functions for simplices, which correspond to weighted projective spaces. to the Zeta-function of Z f over a ﬁnite ﬁeld. 2 Course content 1. The toric compactiﬁcation of Cd with respect to a lattice polytope ∆. The nondegeneracy condition for hypersurfaces Z f ⊂ Cd. The Euler number of Z f. The number of critical points of f in Cd. The Lefschetz-type theorem for Z f. 2. De Rham cohomology of a nondegenerate.

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Get this from a library. On the zeta function of a hypersurface. [Bernard M Dwork; Jean Pierre Serre]. Sasha has already pointed you to the primary source I used some years ago for my "expository" undergraduate thesis on Dwork's Theorem: Koblitz's p-adic Numbers, p-adic Analysis, and Zeta-Functions, which is available in searchable pages here.

I've uploaded a copy of my thesis, which should constitute a relatively easy to digest ~ 50 page write-up of the proof. Zeta Functions of Toric Calabi-Yau Hypersurfaces (Course and Project Description) Daqing Wan March 5, The aim of this course is to apply certain recent developments in Dwork’s p-adic theory to study the p-adic variation of the zeta function attached to a family of aﬃne toric Calabi-Yau hypersurfaces over ﬁnite ﬁelds, leading up toFile Size: 81KB.

If K is a finite field containing the d-th roots of unity, the Galois representation on l-adic cohomology (and so in particular the zeta function) of the hypersurface associated with an arbitrary form of the Fermat equation of degree d is by: 4.

Unspeciﬁed Book Proceedings Series Mirror Symmetry For Zeta Functions Daqing Wan Abstract. In this paper, we study the relation between the zeta function of a Calabi-Yau hypersurface and the zeta function of its mirror.

Two types of arithmetic relations are discovered. This motivates us to formulate two. In mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1 / consider it to be the most important unsolved problem in pure mathematics (Bombieri ).It is of great interest in number theory because it implies results about the distribution of prime numbers.

I am reading Koblitz p-adic analysis book and I am on page The lemma is that $\zeta_{H_f}(T)$ has coefficients in $\mathbb{Z}$. I could follow the rest of the book from page 1 just fine until the proof of this lemma which is horrendously written, probably the worst written proof I seen this month.

zeta functions and p-adic analysis at Kyoto University. These notes are essentially the lecture notes for that course. The first term, I presented several "classical" results on zeta functions in characteristic p Weil's calculation of the zeta.

function of a diagonal hypersurface, Grothendieck's proof of the. We present a new approach to the problem of computing the zeta function of a hypersurface over a finite field.

For a hypersurface defined by a polynomial of degree d in n variables over the field. [1], who compute the zeta function of a projective hypersurface by working in the complement of the hypersurface and using Mumford reduction.

(Indeed, Kedlaya has suggested that there. Donate to arXiv. Please join the Simons Foundation and our generous member organizations in supporting arXiv during our giving campaign September % of your contribution will fund improvements and new initiatives to benefit arXiv's global scientific by: 5.

Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in p-adic cohomology Edgar Costa, David Harvey and Kiran S. Kedlaya We give an interim report on some improvements and generalizations of the Abbott–Kedlaya–Roe method to compute the zeta function of a nondegenerate ample hypersurface in a projectively Cited by: 5.

Vol Issue 1, ISSN: (Print) In this issue (2 articles) OriginalPaper. On the zeta function of a hypersurface. Bernard Dwork Pages OriginalPaper. Endomorphismes complètement continus des espaces de Book Series; Protocols; Reference Works; Proceedings; Other Sites.

; SpringerProtocols. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract. In this paper, we study the relation between the zeta function of a Calabi-Yau hypersurface and the zeta function of its mirror.

Two types of arithmetic relations are discovered. This motivates us to formulate two general arithmetic mirror conjectures for the zeta functions of a mirror pair of Calabi-Yau. If K is a finite field containing the d-th roots of unity, the Galois representation on l-adic cohomology (and so in particular the zeta function) of the hypersurface associated with an arbitrary form of the Fermat equation of degree d is computed.

Sample Chapter(s) Chapter 1: Introduction ( KB) Contents: The Zeta Function; Galois Descent. Koblitz N. () Rationality of the zeta-function of a set of equations over a finite field.

In: p-adic Numbers, p-adic Analysis, and Zeta-Functions. Graduate Texts in Mathematics, vol Author: Neal Koblitz. Algorithmic theory of zeta functions over ﬁnite ﬁelds DAQING WAN ABSTRACT. We give an introductory account of the general algorithmic the-ory of the zeta function of an algebraic set deﬁned over a ﬁnite ﬁeld.

CONTENTS 1. Introduction 2. Generalities on computing zeta functions 3. Reduction to hypersurfaces 4. Hypersurface. Additional Sources for Math Book Reviews; About MAA Reviews; Mathematical Communication; Information for Libraries; Author Resources; Advertise with MAA; Meetings.

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If K is a finite field containing the d-th roots of unity, the Galois representation on l-adic cohomology (and so in particular the zeta function) of the hypersurface associated with an arbitrary form of the Fermat equation of degree d is computed.

This book provides a systematic account of several breakthroughs in the modern theory of zeta functions. It contains two different approaches to introduce and study genuine zeta functions for reductive groups (and their maximal parabolic subgroups) defined over number fields.

Namely, the. Zeta-function regularization When I was a sophomore in Prague, in orDr Ctirad Klimčík (Luminy, France, a specialist in integrability) gave a nice colloquium about string theory.

At that time, I had already studied a lot of stringy NPB papers and preprints on the arXiv but his talk was new and inspiring, anyway.ADS Classic is now deprecated.

It will be completely retired in October Please redirect your searches to the new ADS modern form or the classic info can be found on our blog.