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Exercise 12 in Ch. 1 of Apostol's Modular Functions and Dirichlet Series - How to See The Vanishing of Eisenstein Series

score 64 · Answer 1 · 2026-03-25 09:29:59

64

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Exercise 12 in Ch. 1 of Apostol's Modular Functions and Dirichlet Series - How to See The Vanishing of Eisenstein Series

Published on 25 Mar 2026 - 9:29

score 37 · Answer 2 · 2023-07-07 10:29:56

37

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Solving a system of integral equations of the form $\int_0^r K(r,s)f(s)\mathrm{d}s + \int_r^1 Q(r,s)g(s) \mathrm{d}s = 1$ with $s,r\in[0,1]$

Published on 07 Jul 2023 - 10:29

score 105 · Answer 3 · 2023-07-22 11:08:07

105

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Conformal mapping from triangle to upper half-plane

Published on 22 Jul 2023 - 11:08

score 300 · Answer 4 · 2026-03-26 11:05:23

300

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Conjectured closed forms for Eisenstein-like series

Published on 26 Mar 2026 - 11:05

score 35 · Answer 5 · 2023-08-12 15:18:19

35

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Higher-order 'clover functions' are not elliptic--how to see this?

Published on 12 Aug 2023 - 15:18

score 112 · Answer 6 · 2023-08-14 17:39:04

112

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Rutherford constant and integrals involving elliptic functions: $\displaystyle\int_{0}^{1}\frac{E(x)^2}{K(x)}\mathrm{d}x$

Published on 14 Aug 2023 - 17:39

score 164 · Answer 7 · 2023-08-15 10:07:02

164

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More on Eisenstein-like series.

Published on 15 Aug 2023 - 10:07

score 84 · Answer 8 · 2023-08-15 14:13:10

84

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Trasformation of elliptic integral $\Pi(n;x|m)$ in function of $F(x|m)$ and $E(x|m)$

Published on 15 Aug 2023 - 14:13

score 49 · Answer 9 · 2023-08-23 18:14:57

49

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Elliptic function of the third kind $\Pi(n|m)$ for $n>1$

Published on 23 Aug 2023 - 18:14

score 59 · Answer 10 · 2023-08-28 11:44:40

59

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Found the parameter of the elliptic integral of the first kind

Published on 28 Aug 2023 - 11:44

score 50 · Answer 11 · 2023-09-04 22:28:22

50

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Inversion of the imcomplete elliptic integral of 2nd kind: $E(z|m)=x\;\Longleftrightarrow\; z=\text{bm}(x|m)$

Published on 04 Sep 2023 - 22:28

score 36 · Answer 12 · 2023-09-18 23:03:26

36

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Transcendence of periods of the Weierstrass elliptic function

Published on 18 Sep 2023 - 23:03

score 59 · Answer 13 · 2023-09-20 08:09:22

59

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Prove that the Weiertrass function is biperiodic

Published on 20 Sep 2023 - 8:09

score 158 · Answer 14 · 2023-09-23 10:09:06

158

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Connection between Lame equation with Weierstrass and elliptic sine

Published on 23 Sep 2023 - 10:09

score 13 · Answer 15 · 2026-02-28 22:16:51

13

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Mapping the upper half-plane onto rhombus

Published on 28 Feb 2026 - 22:16

List Question

Exercise 12 in Ch. 1 of Apostol's Modular Functions and Dirichlet Series - How to See The Vanishing of Eisenstein Series

Solving a system of integral equations of the form $\int_0^r K(r,s)f(s)\mathrm{d}s + \int_r^1 Q(r,s)g(s) \mathrm{d}s = 1$ with $s,r\in[0,1]$

Conformal mapping from triangle to upper half-plane

Conjectured closed forms for Eisenstein-like series

Higher-order 'clover functions' are not elliptic--how to see this?

Rutherford constant and integrals involving elliptic functions: $\displaystyle\int_{0}^{1}\frac{E(x)^2}{K(x)}\mathrm{d}x$

More on Eisenstein-like series.

Trasformation of elliptic integral $\Pi(n;x|m)$ in function of $F(x|m)$ and $E(x|m)$

Elliptic function of the third kind $\Pi(n|m)$ for $n>1$

Found the parameter of the elliptic integral of the first kind

Inversion of the imcomplete elliptic integral of 2nd kind: $E(z|m)=x\;\Longleftrightarrow\; z=\text{bm}(x|m)$

Transcendence of periods of the Weierstrass elliptic function

Prove that the Weiertrass function is biperiodic

Connection between Lame equation with Weierstrass and elliptic sine

Mapping the upper half-plane onto rhombus

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