✦ LIBER ✦

Quintic Forms overp-adic Fields

✍ Scribed by David B. Leep; Charles C. Yeomans

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 288 KB
Volume: 57
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1996.0046

No coin nor oath required. For personal study only.

✦ Synopsis

We prove that a quintic form in 26 variables defined over a p-adic field K always has a nontrivial zero over K if the residue class field of K has at least 47 elements. This is in agreement with the theorem of Ax Kochen which states that a homogeneous form of degree d in d 2 +1 variables defined over Q p has a nontrivial Q p -rational zero if p is sufficiently large. The Ax Kochen theorem gives no results on the bound for p. For d=1, 2, 3 it has been known for a long time that there is a nontrivial Q p -rational zero for all values of p. For d=4, Terjanian gave an example of a form in 18 variables over Q 2 having no nontrivial Q 2 -rational zero. This is the first result which gives an effective bound for the case d=5.

📜 SIMILAR VOLUMES

Character Sums overp-adic Fields

✍ Wen-Ching Winnie Li 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 359 KB

that ' v has conductor v. In conclusion, for f =P v , the conductor of the associated ' at v is p r&1 v. Since ' /, f is multiplicative in f, for a general f

p-adic Aspects of Jacobi Forms

✍ Adriana Sofer 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 344 KB

We are interested in understanding and describing the p-adic properties of Jacobi forms. As opposed to the case of modular forms, not much work has been done in this area. The literature includes [3,4,7]. In the first section, we follow Serre's ideas from his theory of p-adic modular forms. We stud

Cross-Sections forp-Adically Closed Fiel

Cross-Sections forp-Adically Closed Fields

✍ Philip Scowcroft 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 194 KB

p-adically closed fields have normalized cross-sections, but no further study of cross-sections was needed to develop the general theory of p-adically closed fields. When studying semialgebraic equivalence relations over Q , I grew p interested in finding a p-adically closed field without a cross-s

Onp-Adic Zeros of Additive Forms of Even

Onp-Adic Zeros of Additive Forms of Even Degree

✍ Hemar Godinho 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 427 KB

In this paper it is proved that the pair f =a 1 x k 1 + } } } +a n x k n , g=b 1 x k 1 + } } } + b n x k n , with k= p { ( p&1) k 0 and (k 0 , p)=1, has a common p-adic zero provided n 2k 2+w( p, {) , where w( p, {)=1Â(log p+(1Â{) log( p&1)). It is also proved that if n 2k 2 , then the pair f, g has

On Bessel Distributions forGL2over ap-Ad

On Bessel Distributions forGL2over ap-Adic Field

✍ Ehud Moshe Baruch 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 358 KB

We show that the Bessel distribution attached by Gelfand and Kazhdan to an infinite-dimensional irreducible admissible representation of G=GL 2 (F ), where F is a non-Archimedean local field, is given by a locally integrable function which is locally constant on an open and dense set of G.

Modular quintics in ℙ4

✍ Christian Meyer 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 142 KB

## Abstract We will examine the arithmetic of some of the members of a pencil of symmetric quintics in projective 4‐space. We will give evidence for the modularity of some of the exceptional members (even the non‐rigid ones) and give a proof in one rigid case. (© 2003 WILEY‐VCH Verlag GmbH & Co. KG