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On a completed generating function of locally harmonic Maass forms
locally harmonic Maass forms indefinite theta functions holomorphic projection mock modular forms modular forms
2012/6/21
While investigating the Doi-Naganuma lift, Zagier defined integral weight cusp forms $f_D$ which are naturally defined in terms of binary quadratic forms of discriminant $D$. It was later determined b...
An ordinary cyclotomic function field
ordinary cyclotomic function field investigate $p$-rank
2012/3/1
In this paper, we investigate the $p$-rank of Jacobian of cyclotomic function field $K_m$. Our goal in this paper is to give the necessary and sufficient condition $m$ such that $K_m$ is ordinary.
A Unified Generating Function of the q-Genocchi Polynomials with their Interpolation Functions
Genocchi numbers and polynomials q-Genocchi numbers and polynomials Number Theory
2011/9/23
Abstract: The purpose of this paper is to construct of the unification q-extension Genocchi polynomials. We give some interesting relations of this type of polynomials. Finally, we derive the q-extens...
Some bounds and limits in the theory of Riemann's zeta function
bounds and limits theory of Riemann's zeta function Number Theory
2011/9/21
Abstract: For any real a>0 we determine the supremum of the real \sigma\ such that \zeta(\sigma+it) = a for some real t. For 0 < a < 1, a = 1, and a > 1 the results turn out to be quite different.}
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An Algorithm to Generate Square-Free Numbers and to Compute the Moebius Function
Mobius function square-free numbers zeta function Riemann hypothesis
2011/9/19
Abstract: We introduce an algorithm that iteratively produces a sequence of natural numbers k_i and functions b_i. The number k_(i+1) arises as the first point of discontinuity of b_i above k_i. We de...
Representation of powers by polynomials over function fields and a problem of Logic
problem of Logic polynomials over function fields Number Theory
2011/9/15
Abstract: We solve a generalization of B\"uchi's problem in any exponent for function fields, and briefly discuss some consequences on undecidability. This provides the first example where this proble...
Congruences for Andrews' spt-function modulo powers of 5, 7 and 13
Andrews' spt-function math
2010/11/15
Congruences are found modulo powers of 5, 7 and 13 for Andrews' smallest parts partition function spt(n). These congruences are reminiscent of Ramanujan's partition congruences modulo powers of 5, 7 a...