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As pointed out in the comments, this is common in number theory. Since the OP wants to write a paper, I give some concrete examples. If you google "Assume the Generalized Riemann Hypothesis" you get 4900 results, including theorems of Hecke (1918), Deuring (1933), Mordell (1934), and Heilbronn (1934) all assuming either the Riemann hypothesis or that it's false. Here is a more recent paper (published in Number Theory) that assumes the generalized RH. Here and here are two other examples, and many more on Google. Hopefully this will help the OP figure out how to write what they want to write.