• Korean Journal of Mathematics
• /
• v.21 no.3
• /
• pp.285-292
• /
• 2013

B. C. Berndt computed the Fourier series of a class of generalized Eisenstein series, which gives an analytic continuation to the generalized Eisenstein series. In this paper, continuing his work, we consider generalized non-holomorphic Eisenstein series and give an analytic continuation to the $s$-plane.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.2
• /
• pp.481-488
• /
• 2020

In this paper we give an exact formula for the Fourier coefficients of the Jacobi-Eisenstein series of square free discriminant lattice index. For a special case the discriminant of lattice is prime we show that the Jacobi-Eisenstein series corresponds to a well known Eisenstein series of modular forms.

• Communications of the Korean Mathematical Society
• /
• v.35 no.1
• /
• pp.63-81
• /
• 2020

In this paper we consider certain classes of generalized level 2 Eisenstein series by simple differential calculations of trigonometric functions. In particular, we give four new transformation formulas for some level 2 Eisenstein series. We can find that these level 2 Eisenstein series are reducible to infinite series involving hyperbolic functions. Moreover, some interesting new examples are given.

• Journal of the Korean Mathematical Society
• /
• v.55 no.3
• /
• pp.507-530
• /
• 2018

It is shown that for a non-unitary twist of a Fuchsian group, which is unitary at the cusps, Eisenstein series converge in some half-plane. It is shown that invariant integral operators provide a spectral decomposition of the space of cusp forms and that Eisenstein series admit a meromorphic continuation.

• Journal of the Chungcheong Mathematical Society
• /
• v.32 no.4
• /
• pp.421-440
• /
• 2019

We establish a few class of infinite series identities from modular transformation formulas for certain series which originally come from generalized non-holomorphic Eisenstein series.

• Honam Mathematical Journal
• /
• v.34 no.3
• /
• pp.391-401
• /
• 2012

B. C. Berndt has found a transformation formula for a large class of functions, which comes from a transformation formula for a more general class of Eisenstein series. In this paper, using his formula which is 'twisted' by change of variables, we find a class of infinite series identities.

• Honam Mathematical Journal
• /
• v.35 no.3
• /
• pp.507-513
• /
• 2013

In this paper, we compute transformation formulae for generalized non-holomorphic Eisenstein series.

• Honam Mathematical Journal
• /
• v.36 no.4
• /
• pp.895-899
• /
• 2014

In this paper, we consider generalized two variable Eisenstein series. We give analytic continuation and prove modular transformation formulae for them.

• Communications of the Korean Mathematical Society
• /
• v.26 no.1
• /
• pp.67-77
• /
• 2011

We find some Eisenstein series related to modulus 4 using a theta function identity of McCullough and Shen and residue theorem for elliptic functions.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.2
• /
• pp.507-514
• /
• 2021

Vector-valued Eisenstein series of weight 3/2 are often not holomorphic. In this paper we prove that, for an even lattice Ḻ, if there exists an odd prime p such that Ḻ is local p-maximal and the determinant of Ḻ is divisible by p2, then the Eisenstein series of weight 3/2 attached to the discriminant form of Ḻ is holomorphic.