On the Number of Vedernikov–Ein Irreducible Components of the Moduli Space of Stable Rank 2 Bundles on the Projective Space

Osipov, Nikolay N.; Тихомиров, С. А.

doi:10.1134/s0037446618010123

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2024

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“…In addition, Osipov and Tikhomirov [11] studied the equation c 2 − 2a 2 = n. Given a positive integer n, denote by P n the number of pairs (c, a) ∈Z 2 with…”

Section: The Equationmentioning

confidence: 99%

Research on the Number of Solutions to a Special Type of Diophantine Equation (ax−1)(by−1) = 2z2

Shu-hui

2023

Mathematics

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Let b be an odd number. By using elementary methods, we prove that: (1) When x is an odd number and y is an even number, the Diophantine equation (2x−1)(by−1)=2z2 has no positive integer solution except when b is two special types of odd number. (2) When x is an odd number and b≡±3(mod8), the Diophantine equation (2x−1)(by−1)=2z2 has no positive integer solution except where b=3 and is another special type of the odd number.

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“…In addition, Osipov and Tikhomirov [11] studied the equation c 2 − 2a 2 = n. Given a positive integer n, denote by P n the number of pairs (c, a) ∈Z 2 with…”

Section: The Equationmentioning

confidence: 99%

Research on the Number of Solutions to a Special Type of Diophantine Equation (ax−1)(by−1) = 2z2

Shu-hui

2023

Mathematics

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Two Series of Components of the Moduli Space of Semistable Reflexive Rank 2 Sheaves on the Projective Space

Kytmanov,

Osipov,

Tikhomirov

2024

Sib Math J

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On the Number of Vedernikov–Ein Irreducible Components of the Moduli Space of Stable Rank 2 Bundles on the Projective Space

Cited by 2 publications

References 10 publications

Research on the Number of Solutions to a Special Type of Diophantine Equation (ax−1)(by−1) = 2z2

Research on the Number of Solutions to a Special Type of Diophantine Equation (ax−1)(by−1) = 2z2

Two Series of Components of the Moduli Space of Semistable Reflexive Rank 2 Sheaves on the Projective Space

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