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A Trigonometric Sum Related to Gauss Sums

score 895 · Answer 1 · 2026-04-14 11:49:25

895

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A Trigonometric Sum Related to Gauss Sums

Published on 14 Apr 2026 - 11:49

score 700 · Answer 2 · 2026-04-16 22:04:01

700

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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 16 Apr 2026 - 22:04

score 27 · Answer 3 · 2026-04-13 07:31:50

27

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Why does the following summation equivalence hold true?

Published on 13 Apr 2026 - 7:31

score 203 · Answer 4 · 2026-04-14 16:13:31

203

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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 Apr 2026 - 16:13

score 291 · Answer 5 · 2026-04-14 11:12:23

291

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Quadratic form Gauss sum and quadratic residue

Published on 14 Apr 2026 - 11:12

score 184 · Answer 6 · 2026-04-11 00:01:31

184

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Quadratic gauss sum equivalence of definition

Published on 11 Apr 2026 - 0:01

score 121 · Answer 7 · 2026-04-13 19:12:45

121

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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 13 Apr 2026 - 19:12

score 147 · Answer 8 · 2026-04-10 22:08:05

147

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Gaussian like sum with binomial coefficients

Published on 10 Apr 2026 - 22:08

score 189 · Answer 9 · 2026-04-09 16:42:03

189

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On the property of Gauss sum

Published on 09 Apr 2026 - 16:42

score 240 · Answer 10 · 2026-04-16 19:50:28

240

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

Published on 16 Apr 2026 - 19:50

score 186 · Answer 11 · 2026-04-15 15:10:20

186

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

Published on 15 Apr 2026 - 15:10

score 193 · Answer 12 · 2026-04-16 15:37:38

193

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

Published on 16 Apr 2026 - 15:37

score 139 · Answer 13 · 2026-04-16 06:56:39

139

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A little bit different quadratic Gauss sum

Published on 16 Apr 2026 - 6:56

score 141 · Answer 14 · 2026-04-09 16:40:52

141

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Formula for twisted generalized quadratic Gauss sums

Published on 09 Apr 2026 - 16:40

score 111 · Answer 15 · 2026-04-17 09:16:54

111

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

Published on 17 Apr 2026 - 9:16

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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