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SOME INDIVISIBILITY PROPERTIES OF GENERALIZED LEFT-FACTORIALS
Kohnen, Winfried Korean Mathematical Society 2018 대한수학회보 Vol.55 No.2
We shall prove certain p-indivisibility properties of so-called generalized left-factorials, where p is a prime.
AN ELEMENTARY PROOF IN THE THEORY OF QUADRATIC RESIDUES
Kohnen, Winfried Korean Mathematical Society 2008 대한수학회보 Vol.45 No.2
We will give a short and elementary proof of the existence of infinitely many primes p such that a given positive integer a congruent 3 modulo 4 is a quadratic non-residue modulo p.
Some indivisibility properties of generalized left-factorials
Winfried Kohnen 대한수학회 2018 대한수학회보 Vol.55 No.2
We shall prove certain $p$-indivisibility properties of so-called generalized left-factorials, where $p$ is a prime.
An elementary proof in the theory of quadratic residues
Winfried Kohnen 대한수학회 2008 대한수학회보 Vol.45 No.2
We will give a short and elementary proof the existence ofinnitely many primes p such that a given positive integer a congruent 3 modulo 4 is a quadratic non-residue modulo p.
SIGN CHANGES OF FOURIER COEFFICIENTS OF ENTIRE MODULAR INTEGRALS
CHOIE, YOUNGJU,KOHNEN, WINFRIED Cambridge University Press 2012 Glasgow mathematical journal Vol.54 No.2
<B>Abstract</B><P>Let <I>f</I> be a non-zero cusp form with real Fourier coefficients <I>a</I>(<I>n</I>) (<I>n</I> ≥ 1) of positive real weight <I>k</I> and a unitary multiplier system <I>v</I> on a subgroup Γ ⊂ <I>SL</I>2(ℝ) that is finitely generated and of Fuchsian type of the first kind. Then, it is known that the sequence (<I>a</I>(<I>n</I>))(<I>n</I> ≥ 1) has infinitely many sign changes. In this short note, we generalise the above result to the case of entire modular integrals of non-positive integral weight <I>k</I> on the group Γ0*(<I>N</I>) (<I>N</I> ∈ ℕ) generated by the Hecke congruence subgroup Γ0(<I>N</I>) and the Fricke involution $W_N:= \big(\scriptsize\begin{array}{c@{}c} 0 & -{1/\sqrt N} \\[3pt] \sqrt N & 0\\ \end{array}\big)$ provided that the associated period functions are polynomials.</P>
On Hecke <i>L</i>-functions attached to half-integral weight modular forms
Choie, YoungJu,Kohnen, Winfried Elsevier 2018 Journal of number theory Vol.189 No.-
<P><B>Abstract</B></P> <P>We investigate non-vanishing properties of L ( f , s ) on the real line, when <I>f</I> is a Hecke eigenform of half-integral weight k + 1 2 on <SUB> Γ 0 </SUB> ( 4 ) .</P>
HOLOMORPHIC DERIVATIVES OF SIEGEL MODULAR FORMS
Hofmann, Eric,Kohnen, Winfried Korean Mathematical Society 2018 대한수학회보 Vol.55 No.5
In this paper, following a criterion of E. Yang and L. Yin we discuss whether on the Siegel half-space of genus $g{\geq}2$ a holomorphic derivative exists.
Transcendence of zeros of Jacobi forms
Choie, Y.,Kohnen, W. Kluwer Academic 2016 RAMANUJAN JOURNAL Vol. No.
<P>A special case of a fundamental theorem of Schneider asserts that if is algebraic (where j is the classical modular invariant), then any zero z not in of the Weierstrass function attached to the lattice is transcendental. In this note we generalize this result to holomorphic Jacobi forms of weight k and index with algebraic Fourier coefficients.</P>