Related papers: Nonexistence of certain classes of generalized ben…

Inspired by a recent work of Mesnager, we present several new infinite families of quadratic ternary bent, near-bent and 2-plateaued functions from some known quadratic ternary bent functions. Meanwhile, the distribution of the Walsh…

We show how Andrews' generating functions for generalized Frobenius partitions can be understood within the theory of Eichler and Zagier as specific coefficients of certain Jacobi forms. This reformulation leads to a recursive process which…

In this paper, we discuss when a class function on a finite group is a bent function. We have found a necessary condition for a class function on a finite abelian group to be bent. Also, we have found a necessary and sufficient condition…

In this paper we introduce the notions of (p,q)-th relative Gol'dberg order and (p,q)-th relative Gol'dberg type of entire functions of several complex variables where p,q are any positive integers. Then we study some growth properties of…

One may consider the generalization of Jacobi polynomials and the Jacobi function of the second kind to a general function where the index is allowed to be a complex number instead of a non-negative integer. These functions are referred to…

In the literature, few $n$-variable rotation symmetric bent functions have been constructed. In this paper, we present two infinite classes of rotation symmetric bent functions on $\mathbb{F}_2^{n}$ of the two forms: {\rm (i)}…

In recent work with Raum the authors considered congruences for the ordinary partition function $p(n)$ of the form $p(\ell Q^r n+\beta)\equiv 0\pmod\ell$ where $\ell, Q\geq 5$ are prime and $r\in \{1,2\}$, and proved a number of results…

Bent functions as optimal combinatorial objects are difficult to characterize and construct. In the literature, bent idempotents are a special class of bent functions and few constructions have been presented, which are restricted by the…

In this article a technique for constructing $p$-ary bent functions from near-bent functions is presented. Two classes of quadratic $p$-ary functions are shown to be near-bent. Applying the construction of bent functions to these classes of…

The coefficients of the generating function $(q;q)^\alpha_\infty$ produce $p_\alpha(n)$ for $\alpha \in \mathbb{Q}$. In particular, when $\alpha = -1$, the partition function is obtained. Recently, Chan and Wang identified and proved…

In this paper we characterize (octal) bent generalized Boolean functions defined on $\BBZ_2^n$ with values in $\BBZ_8$. Moreover, we propose several constructions of such generalized bent functions for both $n$ even and $n$ odd.

We show that while the number of coprime compositions of a positive integer $n$ into $k$ parts can be expressed as a $\mathbb{Q}$-linear combinations of the Jordan totient functions, this is never possible for the coprime partitions of $n$…

We study generalizations of two classical primary constructions of Boolean bent functions, namely the Maiorana-McFarland ($MM$) class and the (Desarguesian) partial spread ($\mathcal{PS}_{ap}$) class. The construction of bent functions…

Let $N\geq 1$ be squarefree with $(N,6)=1$. Let $c\phi_N(n)$ denote the number of $N$-colored generalized Frobenius partition of $n$ introduced by Andrews in 1984. We prove $$ c\phi_N(n)= \sum_{d \mid N} N/d \cdot P\left( \frac{ N}{d^2}n -…

We study the partition function Z_{G(nk,k)}(Q,v) of the Q-state Potts model on the family of (non-planar) generalized Petersen graphs G(nk,k). We study its zeros in the plane (Q,v) for 1<= k <= 7. We also consider two specializations of…

This paper focuses on non-existence results for Cameron-Liebler $k$-sets. A Cameron-Liebler $k$-set is a collection of $k$-spaces in $\mathrm{PG}(n,q)$ or $\mathrm{AG}(n,q)$ admitting a certain parameter $x$, which is dependent on the size…

We obtain new non-existence results of perfect p-ary sequences with period n (called type $[p, n]$). The first case is a class with type [p\equiv5\pmod 8,p^aqn']. The second case contains five types [p\equiv3\pmod 4,p^aq^ln'] for certain…

The derivative of the associated Legendre function of the first kind of integer degree with respect to its order, $\partial P_{n}^{\mu}(z)/\partial\mu$, is studied. After deriving and investigating general formulas for $\mu$ arbitrary…

We generalize Ramanujan's expansions of the fractional-power Euler functions (q^{1/5})_{\infty} = [ J_1 - q^{1/5} + q^{2/5} J_2 ](q^5)_{\infty} and (q^{1/7})_{\infty} = [ J_1 + q^{1/7} J_2 - q^{2/7} + q^{5/7} J_3 ] (q^7)_{\infty} to…

Bent-negabent functions have many important properties for their application in cryptography since they have the flat absolute spectrum under the both Walsh-Hadamard transform and nega-Hadamard transform. In this paper, we present four new…