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About 10,000 papers for “Arithmetic function”

On A New Arithmetic Function

Priyam Das, Kanishka Chowdhury · Journal of Mathematics and System Science · 2017

Here we explore some fundamental aspects of what may be termed as a new arithmetic function (defined notionally as the T function) together with its possible inverse (T -1 ), as it is not in frequent discussion among the number theorists.

Cited by 0Open access

Arithmetic of abelian function fields

Tiphaine Beaumont · theses.fr (ABES) · 2022

L'objectif de cette thèse est l'obtention de formules de classes équivariantes dans différents contextes : d'une part lorsque A = F_q[θ], G est un groupe abélien fini et E est un module d'Anderson et d'autre part lorsque A est général, d_\infty = 1, G est un groupe d'ordre premier à p et E est un module d'Anderson admissible.

Cited by 0Open access

ARITHMETIC OF THE PARTITION FUNCTION

Ken Dnd · 2001

Partitions have played an important role in many aspects of combinatories, Lie theory, physics, and representation theory. Here we describe some of the recent discoveries regarding the arithmetic of the partition function, including a relationship between partitions and Tate-Shafarevich groups of modular motives in arithmetic algebraic geometry. Euler [4] showed that the generating function for p(n) is given by the convenient infinite product

Cited by 0

Arithmetic properties of DSOME function

Nayandeep Deka Baruah, Pankaj Gogoi · ArXiv.org · 2026

Recently, Andrews and Ghosh Dastidar (Ramanujan J. \textbf{69}, Art. No. 26, 2026) studied two interesting functions $SOME(n)$ and $DSOME(n)$, where $SOME(n)$ is the sum of all the odd parts in the partitions of $n$ minus the sum of all even parts and $DSOME(n)$ is the sum of all the odd parts in the partitions of $n$ into distinct parts minus sum of all the even parts. They expressed the generating functions of $SOME(n)$ and $DSOME(n)$ in terms of $q$-series and found several interesting congruences modulo 4 and 5. In this paper, we express the generating function of $DSOME(n)$ in a closed form, which allows us to find some new congruences and internal congruences modulo 4 and 8 for $DSOME(n)$.

Cited by 0Open access

Arithmetic of function field units

Bruno Anglès, Floric Tavares Ribeiro · arXiv (Cornell University) · 2015

We prove a "discrete analogue" for Taelman's class modules of certain Conjectures formulated by R. Greenberg for cyclotomic fields.

Cited by 1Open access

On a new arithmetic function

Krassimir Atanassov, József Sándor · Notes on Number Theory and Discrete Mathematics · 2018

A new arithmetic function is introduced and its basic properties are studied. Some inequalities between the new and some other arithmetic functions are formulated and proved.

Cited by 2Open access

Arithmetic of the Fabius Function

Arias de Reyna, J. · Zenodo (CERN European Organization for Nuclear Research) · 2018

See the abstract in the attached pdf.

Cited by 0Open access

Arithmetic properties of DSOME function

Nayandeep Deka Baruah, Pankaj Gogoi · arXiv (Cornell University) · 2026

Recently, Andrews and Ghosh Dastidar (Ramanujan J. \textbf{69}, Art. No. 26, 2026) studied two interesting functions $SOME(n)$ and $DSOME(n)$, where $SOME(n)$ is the sum of all the odd parts in the partitions of $n$ minus the sum of all even parts and $DSOME(n)$ is the sum of all the odd parts in the partitions of $n$ into distinct parts minus sum of all the even parts. They expressed the generating functions of $SOME(n)$ and $DSOME(n)$ in terms of $q$-series and found several interesting congruences modulo 4 and 5. In this paper, we express the generating function of $DSOME(n)$ in a closed form, which allows us to find some new congruences and internal congruences modulo 4 and 8 for $DSOME(n)$.

Cited by 0Open access

Arithmetic of the Fabius Function

Arias de Reyna, J. · Zenodo (CERN European Organization for Nuclear Research) · 2018

See the abstract in the attached pdf.

Cited by 0Open access

On Arithmetic Over Function Fields

李亭芳 · 2013

There are two parts in this dissertation. The first part (Chapter 1) is trace formula of a Brandt matrix. Given a division quaternion algebra over a global function field which is definite with respect a fixed chosen infinity place. A family of Brandt matrices is then introduced to encode information from the arithmetic of the division quaternion algebra. Adapting Eichler’s method from the rational field case, we build up a fine formula expressing the trace of these Brandt matrices in terms of class numbers of specific orders inside imaginary quadratic extensions of the global function field embeddable into the division quaternion. The proof is base on a detailed study of the so-called optimal embeddings of quadratic orders into the division quaternion. The second part (Chapter 2 and 3) is multiple Dirichlet series over a global function field. Fisher and Friedberg [c.f. FF and FF2] constructed and studied a family of multiple (2 and 3 variables) Dirichlet series over general function fields. They proved that these multiple Dirichlet series satisfy finite, non-abelian groups of functional equations and are rational functions with specific denominator. We then are interested in explicitly finding these multiple Dirichlet series over a curve. In the 2-variable case, we work on in particular the elliptic curve C : y^2 = x^3 + 2x over F_5. For the 3-variable case, we compute the curve P^1 over F_q with q odd which the function field is rational function field over F_q.

Cited by 1