Orbital L-functions for the Space of Binary Cubic Forms

AbstractWe introduce the notion of orbital L-functions for the space of binary cubic forms and investigate their analytic properties. We study their functional equations and residue formulas in some detail. Aside from their intrinsic interest, the results from this paper are used to prove the existence of secondary terms in counting functions for cubic fields. This is worked out in a companion paper.

Download Full-text

Identities for field extensions generalizing the Ohno–Nakagawa relations

Compositio Mathematica ◽

10.1112/s0010437x15007411 ◽

2015 ◽

Vol 151 (11) ◽

pp. 2059-2075 ◽

Cited By ~ 4

Author(s):

Henri Cohen ◽

Simon Rubinstein-Salzedo ◽

Frank Thorne

Keyword(s):

Vector Space ◽

Functional Equations ◽

Zeta Functions ◽

Reflection Principle ◽

Galois Groups ◽

Field Extensions ◽

Prehomogeneous Vector Space ◽

Counting Functions ◽

Cubic Fields ◽

Cubic Forms

In previous work, Ohno conjectured, and Nakagawa proved, relations between the counting functions of certain cubic fields. These relations may be viewed as complements to the Scholz reflection principle, and Ohno and Nakagawa deduced them as consequences of ‘extra functional equations’ involving the Shintani zeta functions associated to the prehomogeneous vector space of binary cubic forms. In the present paper, we generalize their result by proving a similar identity relating certain degree-$\ell$ fields to Galois groups $D_{\ell }$ and $F_{\ell }$, respectively, for any odd prime $\ell$; in particular, we give another proof of the Ohno–Nakagawa relation without appealing to binary cubic forms.

Download Full-text

Secondary terms in counting functions for cubic fields

Duke Mathematical Journal ◽

10.1215/00127094-2371752 ◽

2013 ◽

Vol 162 (13) ◽

pp. 2451-2508 ◽

Cited By ~ 24

Author(s):

Takashi Taniguchi ◽

Frank Thorne

Keyword(s):

Counting Functions ◽

Cubic Fields

Download Full-text

On Diophantine approximations of the solutions of q-functional equations

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210502000331 ◽

2002 ◽

Vol 132 (03) ◽

pp. 639

Keyword(s):

Functional Equations ◽

Diophantine Approximations

Download Full-text

Traditional masculinity, help avoidance, and intrinsic interest in relation to high school students’ English and math performance.

Psychology of Men & Masculinity ◽

10.1037/men0000188 ◽

2019 ◽

Vol 20 (4) ◽

pp. 603-611

Author(s):

Campbell Leaper ◽

Timea Farkas ◽

Christy R. Starr

Keyword(s):

High School ◽

High School Students ◽

Math Performance ◽

School Students ◽

Intrinsic Interest ◽

Traditional Masculinity

Download Full-text

On some functional equations related to derivations and bicircular projections in rings

Glasnik Matematicki ◽

10.3336/gm.49.2.06 ◽

2014 ◽

Vol 49 (2) ◽

pp. 313-331

Author(s):

Maja Fošner ◽

◽

Benjamin Marcen ◽

Nejc Širovnik ◽

Joso Vukman ◽

...

Keyword(s):

Functional Equations

Download Full-text

Functional equations related to weightable quasi-metrics

Hacettepe Journal of Mathematics and Statistics ◽

10.15672/hjms.2015449441 ◽

2015 ◽

Vol 4 (1047) ◽

Author(s):

M.J. Campion ◽

E. Indurain ◽

G. Ochoa

Keyword(s):

Functional Equations

Download Full-text

Solutions and Stability of Generalized Mixed Type QCA-Functional Equations in Random Normed Spaces

Annals of the Alexandru Ioan Cuza University - Mathematics ◽

10.2478/v10157-012-0047-2 ◽

2013 ◽

Vol 59 (2) ◽

pp. 299-320

Author(s):

M. Eshaghi Gordji ◽

Y.J. Cho ◽

H. Khodaei ◽

M. Ghanifard

Keyword(s):

Functional Equation ◽

General Solution ◽

Functional Equations ◽

Mixed Type ◽

Additive Functional ◽

Normed Spaces ◽

Additive Functional Equation ◽

Probabilistic Normed Spaces ◽

Random Normed Spaces ◽

Generalized Stability

Abstract In this paper, we investigate the general solution and the generalized stability for the quartic, cubic and additive functional equation (briefly, QCA-functional equation) for any k∈ℤ-{0,±1} in Menger probabilistic normed spaces.

Download Full-text

Identities related to special polynomials and combinatorial numbers

Filomat ◽

10.2298/fil1715833y ◽

2017 ◽

Vol 31 (15) ◽

pp. 4833-4844 ◽

Cited By ~ 2

Author(s):

Eda Yuluklu ◽

Yilmaz Simsek ◽

Takao Komatsu

Keyword(s):

Generating Functions ◽

Functional Equations ◽

Stirling Numbers ◽

Bernoulli Numbers ◽

Euler Numbers ◽

Special Polynomials ◽

Central Factorial Numbers

The aim of this paper is to give some new identities and relations related to the some families of special numbers such as the Bernoulli numbers, the Euler numbers, the Stirling numbers of the first and second kinds, the central factorial numbers and also the numbers y1(n,k,?) and y2(n,k,?) which are given Simsek [31]. Our method is related to the functional equations of the generating functions and the fermionic and bosonic p-adic Volkenborn integral on Zp. Finally, we give remarks and comments on our results.

Download Full-text