scholarly journals On the representation of integers by indefinite binary Hermitian forms

2011 ◽  
Vol 43 (6) ◽  
pp. 1048-1058 ◽  
Author(s):  
Jouni Parkkonen ◽  
Frédéric Paulin
Keyword(s):  
Hermitian Forms ◽  
Representation Of Integers

scholarly journals Counting and equidistribution in quaternionic Heisenberg groups

2021 ◽  
pp. 1-38
Author(s):  
JOUNI PARKKONEN ◽  
FRÉDÉRIC PAULIN
Keyword(s):  
Hyperbolic Geometry ◽  
Quaternion Algebra ◽  
Rational Points ◽  
Hyperbolic Spaces ◽  
Heisenberg Groups ◽  
Arithmetic Groups ◽  
Hermitian Forms ◽  
Dimension 2 ◽  
Counting Formula ◽  
The Relationship

Abstract We develop the relationship between quaternionic hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on quaternionic hyperbolic spaces, especially in dimension 2. We prove a Mertens counting formula for the rational points over a definite quaternion algebra A over ${\mathbb{Q}}$ in the light cone of quaternionic Hermitian forms, as well as a Neville equidistribution theorem of the set of rational points over A in quaternionic Heisenberg groups.

Non unimodular Hermitian forms

1996 ◽  
Vol 123 (1) ◽  
pp. 233-240 ◽  
Author(s):  
Eva Bayer-Fluckiger ◽  
Laura Fainsilber
Keyword(s):  
Hermitian Forms

Spherical functions and local densities on the space of p-adic quaternion Hermitian forms

2021 ◽  
pp. 1-38
Author(s):  
Yumiko Hironaka
Keyword(s):  
Laurent Polynomial ◽  
Spherical Functions ◽  
Plancherel Formula ◽  
Explicit Formulas ◽  
Hermitian Forms ◽  
Spherical Fourier Transform ◽  
Local Densities ◽  
Laurent Polynomial Ring ◽  
Injective Map ◽  
Residual Characteristic

We introduce the space [Formula: see text] of quaternion Hermitian forms of size [Formula: see text] on a [Formula: see text]-adic field with odd residual characteristic, and define typical spherical functions [Formula: see text] on [Formula: see text] and give their induction formula on sizes by using local densities of quaternion Hermitian forms. Then, we give functional equation of spherical functions with respect to [Formula: see text], and define a spherical Fourier transform on the Schwartz space [Formula: see text] which is Hecke algebra [Formula: see text]-injective map into the symmetric Laurent polynomial ring of size [Formula: see text]. Then, we determine the explicit formulas of [Formula: see text] by a method of the author’s former result. In the last section, we give precise generators of [Formula: see text] and determine all the spherical functions for [Formula: see text], and give the Plancherel formula for [Formula: see text].

On the representation of integers as sums of triangular numbers

1995 ◽  
Vol 50 (1-2) ◽  
pp. 73-94 ◽  
Author(s):  
Ken Ono ◽  
Sinai Robins ◽  
Patrick T. Wahl
Keyword(s):  
Triangular Numbers ◽  
Representation Of Integers

scholarly journals The Weight Distribution of a Class of Cyclic Codes Related to Hermitian Forms Graphs

2013 ◽  
Vol 59 (5) ◽  
pp. 3064-3067 ◽  
Author(s):  
Shuxing Li ◽  
Sihuang Hu ◽  
Tao Feng ◽  
Gennian Ge
Keyword(s):  
Weight Distribution ◽  
Cyclic Codes ◽  
Hermitian Forms
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