Addressing professors over email

Question

How does one start an email to a professor? I am curious about how it is done in Russia, but also how it should be done in Russian in the United States. Over here, especially in small classes (like my Russian class), we have relatively casual relationships with professors. In an English email, I would say, "Hello Professor Smith."

Answer 1

I'd start an official message with:

Уважаемый Имя Отчество!

or alternatively:

Уважаемый профессор Фамилия!

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In the case of a closer relationship, I'd use:

Здравствуйте, Имя Отчество!
Здравствуйте, профессор Фамилия!

Answer 2

If your relationship is casual and less formal one may be addressed as

Приветствую/Здравствуйте, профессор ^{no (sur)names}

Omission of a name underscores the informality and sounds kind of cheery, merry, enthusiastic and upbeat. And if the content of the message is somber or deals with a request of some sort, then it conversely sounds more appealing, cordial, intimate, hopeful and ingratiating.