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math.CA2019★ 1 cited
Trigonometric identities and quadratic residues
Zhi-Wei Sun
In this paper we obtain some novel identities involving trigonometric functions. Let be any positive odd integer. We show that $$\sum_{r=0}^{n-1}\frac1{1+\sin2π\frac{x+r}n+\cos…
math.NT2019★ 2 cited
On some determinants involving the tangent function
Zhi-Wei Sun
Let be an odd prime and let with . In this paper we mainly evaluate $$T_p^{(δ)}(a,b,x):=\det\left[x+\tanπ\frac{aj^2+bk^2}p\right]_{δ\le j,k\le (p-1…