Question

A Trigonometric Sum Related to Gauss Sums

score 892 · Answer 1 · 2013-03-28 05:45:09

892

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A Trigonometric Sum Related to Gauss Sums

Published on 28 Mar 2013 - 5:45

score 697 · Answer 2 · 2020-08-27 14:32:40

697

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Prove that $\sum _{x=0}^{p-1}e^{\frac {2\pi ix^{2}}{p}}={\sqrt {p}} $ , $ p \equiv 1{\pmod {4}}$

Published on 27 Aug 2020 - 14:32

score 24 · Answer 3 · 2020-10-01 16:13:39

24

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Why does the following summation equivalence hold true?

Published on 01 Oct 2020 - 16:13

score 200 · Answer 4 · 2020-11-14 21:25:23

200

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Prove a formula to evaluate Legendre Symbol $(\frac{-3}{p})$ using quadratic Gauss Sums (i.e. without using quadratic reciprocity)

Published on 14 Nov 2020 - 21:25

score 288 · Answer 5 · 2020-11-23 22:40:36

288

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Quadratic form Gauss sum and quadratic residue

Published on 23 Nov 2020 - 22:40

score 181 · Answer 6 · 2020-11-27 11:22:21

181

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Quadratic gauss sum equivalence of definition

Published on 27 Nov 2020 - 11:22

score 118 · Answer 7 · 2020-12-21 05:23:02

118

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Understanding the proofs in "Elementary aspects of the Verlinde formula and of the Harder–Narasimhan–Atiyah–Bott formula" from Don Zagier

Published on 21 Dec 2020 - 5:23

score 144 · Answer 8 · 2021-01-11 18:01:40

144

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Gaussian like sum with binomial coefficients

Published on 11 Jan 2021 - 18:01

score 188 · Answer 9 · 2026-02-23 09:09:43

188

Views

On the property of Gauss sum

Published on 23 Feb 2026 - 9:09

score 237 · Answer 10 · 2021-03-26 21:58:58

237

Views

Number of solutions to $x^3 + y^3 + z^3 + t^3 = 0 \pmod p$

Published on 26 Mar 2021 - 21:58

score 183 · Answer 11 · 2021-06-10 15:45:07

183

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Covariance of geometric Brownian motion via first and second moments and MGFs

Published on 10 Jun 2021 - 15:45

score 190 · Answer 12 · 2021-07-07 17:48:57

190

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Show that the quadratic Gauss sum can be simplified by completing the square

Published on 07 Jul 2021 - 17:48

score 136 · Answer 13 · 2021-08-24 22:30:28

136

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A little bit different quadratic Gauss sum

Published on 24 Aug 2021 - 22:30

score 140 · Answer 14 · 2026-02-23 09:07:31

140

Views

Formula for twisted generalized quadratic Gauss sums

Published on 23 Feb 2026 - 9:07

score 108 · Answer 15 · 2021-09-13 14:13:51

108

Views

Why does the quadratic Gauss sum $G(a,b,c)$ evaluate to 0 when $gcd(a,c)>1$?

Published on 13 Sep 2021 - 14:13

List Question

A Trigonometric Sum Related to Gauss Sums

Prove that $\sum _{x=0}^{p-1}e^{\frac {2\pi ix^{2}}{p}}={\sqrt {p}} $ , $ p \equiv 1{\pmod {4}}$

Why does the following summation equivalence hold true?

Prove a formula to evaluate Legendre Symbol $(\frac{-3}{p})$ using quadratic Gauss Sums (i.e. without using quadratic reciprocity)

Quadratic form Gauss sum and quadratic residue

Quadratic gauss sum equivalence of definition

Understanding the proofs in "Elementary aspects of the Verlinde formula and of the Harder–Narasimhan–Atiyah–Bott formula" from Don Zagier

Gaussian like sum with binomial coefficients

On the property of Gauss sum

Number of solutions to $x^3 + y^3 + z^3 + t^3 = 0 \pmod p$

Covariance of geometric Brownian motion via first and second moments and MGFs

Show that the quadratic Gauss sum can be simplified by completing the square

A little bit different quadratic Gauss sum

Formula for twisted generalized quadratic Gauss sums

Why does the quadratic Gauss sum $G(a,b,c)$ evaluate to 0 when $gcd(a,c)>1$?

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