Some mixed character sum identities of Katz II

Ron Evans; John Greene

doi:10.1007/s40993-016-0071-5

Some mixed character sum identities of Katz II

Ron Evans, John Greene

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

A conjecture connected with quantum physics led N. Katz to discover some amazing mixed character sum identities over a field of q elements, where q is a power of a prime p> 3. His proof required deep algebro-geometric techniques, and he expressed interest in finding a more straightforward direct proof. The first author recently gave such a proof of his identities when q≡1(mod4), and this paper provides such a proof for the remaining case q≡3(mod4). Our proofs are valid for all characteristics p> 2. Along the way we prove some elegant new character sum identities.

Original language	English (US)
Article number	8
Journal	Research in Number Theory
Volume	3
Issue number	1
DOIs	https://doi.org/10.1007/s40993-016-0071-5
State	Published - Dec 1 2017

Bibliographical note

Publisher Copyright:
© 2017, The Author(s).

Keywords

Eisenstein sums
Gauss and Jacobi sums
Hasse–Davenport theorems
Hypergeometric F character sums over finite fields
Norm-restricted Gauss and Jacobi sums
Quantum physics

Publisher link

10.1007/s40993-016-0071-5

Find It

Find It at U of M Libraries

Cite this

@article{f49fa74f8a4349ef90a07aac3f40d389,

title = "Some mixed character sum identities of Katz II",

abstract = "A conjecture connected with quantum physics led N. Katz to discover some amazing mixed character sum identities over a field of q elements, where q is a power of a prime p> 3. His proof required deep algebro-geometric techniques, and he expressed interest in finding a more straightforward direct proof. The first author recently gave such a proof of his identities when q≡1(mod4), and this paper provides such a proof for the remaining case q≡3(mod4). Our proofs are valid for all characteristics p> 2. Along the way we prove some elegant new character sum identities.",

keywords = "Eisenstein sums, Gauss and Jacobi sums, Hasse–Davenport theorems, Hypergeometric F character sums over finite fields, Norm-restricted Gauss and Jacobi sums, Quantum physics",

author = "Ron Evans and John Greene",

note = "Publisher Copyright: {\textcopyright} 2017, The Author(s).",

year = "2017",

month = dec,

day = "1",

doi = "10.1007/s40993-016-0071-5",

language = "English (US)",

volume = "3",

journal = "Research in Number Theory",

issn = "2363-9555",

publisher = "Springer Open",

number = "1",

}

TY - JOUR

T1 - Some mixed character sum identities of Katz II

AU - Evans, Ron

AU - Greene, John

PY - 2017/12/1

Y1 - 2017/12/1

N2 - A conjecture connected with quantum physics led N. Katz to discover some amazing mixed character sum identities over a field of q elements, where q is a power of a prime p> 3. His proof required deep algebro-geometric techniques, and he expressed interest in finding a more straightforward direct proof. The first author recently gave such a proof of his identities when q≡1(mod4), and this paper provides such a proof for the remaining case q≡3(mod4). Our proofs are valid for all characteristics p> 2. Along the way we prove some elegant new character sum identities.

AB - A conjecture connected with quantum physics led N. Katz to discover some amazing mixed character sum identities over a field of q elements, where q is a power of a prime p> 3. His proof required deep algebro-geometric techniques, and he expressed interest in finding a more straightforward direct proof. The first author recently gave such a proof of his identities when q≡1(mod4), and this paper provides such a proof for the remaining case q≡3(mod4). Our proofs are valid for all characteristics p> 2. Along the way we prove some elegant new character sum identities.

KW - Eisenstein sums

KW - Gauss and Jacobi sums

KW - Hasse–Davenport theorems

KW - Hypergeometric F character sums over finite fields

KW - Norm-restricted Gauss and Jacobi sums

KW - Quantum physics

UR - http://www.scopus.com/inward/record.url?scp=85020005726&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85020005726&partnerID=8YFLogxK

U2 - 10.1007/s40993-016-0071-5

DO - 10.1007/s40993-016-0071-5

M3 - Article

AN - SCOPUS:85020005726

SN - 2363-9555

VL - 3

JO - Research in Number Theory

JF - Research in Number Theory

IS - 1

M1 - 8

ER -

Some mixed character sum identities of Katz II

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this