Results 21 to 30 of about 1,390 (102)
Proving some identities of Gosper on $q$-trigonometric functions
, 2018 Gosper introduced the functions $\sin_q z$ and $\cos_q z$ as $q$-analogues for the trigonometric functions $\sin z$ and $\cos z$ respectively. He stated but did not prove a variety of identities involving these two $q$-trigonometric functions.
Bachraoui, Mohamed El
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Cycle integrals and rational period functions for Γ0+(2) and Γ0+(3)
Open MathematicsFor p∈{2,3}p\in \left\{2,3\right\} and an even integer kk, let Wk−2−(p){W}_{k-2}^{-}\left(p) be the space of period polynomials of weight k−2k-2 on Γ0+(p){\Gamma }_{0}^{+}\left(p) with eigenvalue −1-1 under the Fricke involution.
Choi SoYoung +2 more
doaj +1 more source
The tenth order mock theta functions revisited
, 2009 In this paper we consider the first four of the eight identities between the tenth order mock theta functions, found in Ramanujan's lost notebook. These were originally proved by Choi.
Zwegers, Sander
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On the common zeros of quasi-modular forms for Γ+0(N) of level N = 1, 2, 3
Open MathematicsIn this article, we study common zeros of the iterated derivatives of the Eisenstein series for Γ0+(N){\Gamma }_{0}^{+}\left(N) of level N=1,2,and2,N=1,2, and 3, which are quasi-modular forms.
Im Bo-Hae, Kim Hojin, Lee Wonwoong
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Amplification arguments for large sieve inequalities
, 2010 We present a new proof of the "arithmetic" large sieve inequality, starting from the corresponding "harmonic" inequality, which is based on an amplification idea.
Kowalski, Emmanuel
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Recurrence relations satisfied by some arithmetic groups
Open MathematicsRecently, recurrence relations satisfied by the modular traces of the Hauptmodul for Γ0(N){\Gamma }_{0}\left(N) of genus zero have been established. However, these relations do not determine all values of the modular traces.
Kang Hee Doo +2 more
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Differential equations for septic theta functions
, 2013 We demonstrate that quotients of septic theta functions appearing in S. Ramanujan's Notebooks and in F. Klein's work satisfy a new coupled system of nonlinear differential equations with interesting symmetric form.
Huber, Tim, Lara, Danny
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On a completed generating function of locally harmonic Maass forms
, 2014 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 $D$.
Ben Kane +8 more
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, 2013 Let $k$ be an odd integer $\ge 3$ and $N$ a positive integer such that $4 \mid N$. Let $\chi$ be an even Dirichlet character modulo $N$. Shimura decomposes the space of half-integral weight cusp forms $S_{k/2}(N,\chi)$ as a direct sum of $S_0(N,\chi ...
Kohnen W. +3 more
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Conformation-specific Antibodies Targeting Aggregated Forms of α-synuclein Block the Propagation of Synucleinopathy. [PDF]
Exp Neurobiol, 2022 Choi M +10 more
europepmc +1 more source