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We provide estimates for the exponential sum

Ternary cyclotomic polynomials are polynomials of the form Φpqr(z) = ∏ ρ(z − ρ), where p < q < r are odd primes and the product is taken over all primitive pqr-th roots of unity ρ. We show that for every p there exists an infinite family of polynomials Φpqr such that the set of coefficients of each of these polynomials coincides with the set of integers in… (More)

- Gennady Bachman
- 2010

Taking a combinatorial point of view on cyclotomic polynomials leads to a larger class of polynomials we shall call the inclusion-exclusion polynomials. This gives a more appropriate setting for certain types of questions about the coefficients of these polynomials. After establishing some basic properties of inclusion-exclusion polynomials we turn to a… (More)

- Gennady Bachman, Ebrahim Salehi, NV
- 2007

Given an abelian group A, a graph G is said to be A-magic if there exists a labeling l : E(G) → A− {0} such that the induced vertex labeling l : V (G) → A defined by l(v) = ∑

- Gennady Bachman, Reid S Barker
- The Journal of organic chemistry
- 1949

- Gennady Bachman, G M Picha
- Journal of the American Chemical Society
- 1946

- Gennady Bachman, DAVID E. WELTON
- The Journal of organic chemistry
- 1947

- Gennady Bachman, H H Szmant
- Journal of the American Chemical Society
- 1946

- Gennady Bachman, DAVID E. WELTON
- Journal of the American Chemical Society
- 1947

- Gennady Bachman, Janice Wood Wetzel
- The Journal of organic chemistry
- 1946