List questions from theta-functions

Published on 16 Aug 2016 - 22:54

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what is the expansion for $\log \sum q^{n^2}$?

Published on 25 Mar 2026 - 6:10

174

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Evaluate $\sum\limits_{n=0}^\infty n^ke^{-an^2}$ and $\sum\limits_{n=0}^\infty(-1)^nn^ke^{-an^2}$ .

Published on 06 Sep 2016 - 12:17

76

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integrals of theta functions on tori

Published on 07 Sep 2016 - 15:31

69

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Equality regarding $\vartheta$-functions using Poisson Summation

Published on 06 Oct 2016 - 1:38

79

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Find $\beta \overline{\beta}$ for $\beta \equiv 1 \mod \sqrt{-7}$ in $\mathbb{Q}(\sqrt{-7})$

Published on 10 Oct 2016 - 18:35

109

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Theta Functions which never vanish

Published on 04 Nov 2016 - 22:11

35

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A simple identity for Thetaseries

Published on 23 Nov 2016 - 0:45

41

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Another simple Thetaseries identity.

Published on 23 Nov 2016 - 1:26

68

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Big-Theta sum rule proof

Published on 30 Nov 2016 - 6:09

204

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How to evaluate $\int_0^x\vartheta_3(0,t)\ dt$?

Published on 01 Jan 2017 - 15:30

118

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Integrating modular theta function of real quadratic field

Published on 03 Jan 2017 - 13:41

178

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Closed-form of an integral involving a Jacobi theta function, $ \int_0^{t} \theta_3(e^{-\pi^2 (t-\tau)}) \, \theta_2(e^{-\pi^2 \tau}) \ d\tau =1$

Published on 03 Jan 2017 - 20:11

505

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On $x^3+y^3=z^3$, the Dixonian elliptic functions, and the Borwein cubic theta functions

Published on 09 Jan 2017 - 16:42

243

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How to prove that this iterated mean gives $\frac{2 \cdot 2^{7/8}}{\vartheta _2\left(0,\frac{1}{\sqrt{2}}\right)}$ for $a_0=2,b_0=1$?

Published on 24 Jan 2017 - 13:50

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What does the Hecke bound $|a_n| < C n$ say about $\theta(z)^4$?

what is the expansion for $\log \sum q^{n^2}$?

Evaluate $\sum\limits_{n=0}^\infty n^ke^{-an^2}$ and $\sum\limits_{n=0}^\infty(-1)^nn^ke^{-an^2}$ .

integrals of theta functions on tori

Equality regarding $\vartheta$-functions using Poisson Summation

Find $\beta \overline{\beta}$ for $\beta \equiv 1 \mod \sqrt{-7}$ in $\mathbb{Q}(\sqrt{-7})$

Theta Functions which never vanish

A simple identity for Thetaseries

Another simple Thetaseries identity.

Big-Theta sum rule proof

How to evaluate $\int_0^x\vartheta_3(0,t)\ dt$?

Integrating modular theta function of real quadratic field

Closed-form of an integral involving a Jacobi theta function, $ \int_0^{t} \theta_3(e^{-\pi^2 (t-\tau)}) \, \theta_2(e^{-\pi^2 \tau}) \ d\tau =1$

On $x^3+y^3=z^3$, the Dixonian elliptic functions, and the Borwein cubic theta functions

How to prove that this iterated mean gives $\frac{2 \cdot 2^{7/8}}{\vartheta _2\left(0,\frac{1}{\sqrt{2}}\right)}$ for $a_0=2,b_0=1$?

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