Summary:

Our look at some of the stories in mobile today: Amazon (NSDQ: AMZN) looks to get Apple’s “Appstore” suit thrown out; Microsoft (NSDQ: MSFT)…

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Our look at some of the stories in mobile today: Amazon (NSDQ: AMZN) looks to get Apple’s “Appstore” suit thrown out; Microsoft (NSDQ: MSFT) works on a native check-in service for Windows Phone 7; Twitter on mobile ambition; Foursquare funding.

Amazon v. Apple: Some progress, of sorts, on the lawsuit that Apple (NSDQ: AAPL) has filed against Amazon over the “Appstore” brand name that Amazon has used for its Amazon mobile apps storefront. Yesterday, Amazon filed documents seeking to get the case closed, citing evidence from Apple CEO Steve Jobs himself referring generically to storefronts selling apps as “app stores.” If this sounds familiar, it’s because it is the same evidence that Microsoft is using it its case against Apple, in which it wants to establish that the term “app store” is, in fact, a generic concept and cannot be trademarked. You can read Amazon’s most recent filing here (via GeekWire). Both cases continue.

Windows Phone 7: A neat feature might be coming in an update to Windows Phone 7 in the future: a native check-in service, similar to the kind that you see already in popular apps like Foursquare, Gowalla and Facebook. It would run as an extension of the Windows Live service, and by being native to the OS, potentially the service could be a lot more integrated with other services — and hence more useful. It is the sort of service that, frankly, seems like a no-brainer for Microsoft and one that it should have been offering from the word go — given how much more that Microsoft does could be linked up with the check-in as a result (eg messaging, email, and even mobile advertising).

The check-in conjecture is based on a Tweet from a Windows software tester, Ken Dacey, which said: “Doing testing of Windows Phone. (Checked in at Microsoft Studio F) via a WindowsLive client. It was then picked up by MobileTechWorld; and tellingly, that tweet has since been deleted.

The blog further guesses that this could be part of the “Mango” update to WP7 that is scheduled for later this year.

Foursquare: Apropos of Microsoft’s move on check-ins, that space could be getting some attention elsewhere, too. The WSJ is reporting that Foursquare is currently raising funding — the target is $20 million to $40 million — that would give the company a valuation of up to $500 million. That’s a $400 million increase on last summer’s valuation, when Foursquare picked up $20 million from Andreessen Horowitz and other VCs.

Twitter: Some statistics on how strongly mobile figures for the microblogging service at the moment. Some 40 percent of tweets currently come from mobile devices; and in the first three month of this year, mobile signups increased by 50 percent. (It’s not clear, though, if that relates to people downloading Twitter’s own mobile apps or if that also includes all the third-party Twitter interfaces such as those made by Uber Media.) The numbers come from Michael Abbott, Twitter’s VP of engineering, speaking at the Venture Beat mobile conference in San Francisco.

Abbott said that mobile, along with discovery and relevance, are the company’s three main areas of product focus at the moment, although he didn’t go so far as to reveal what that could mean in terms of actual mobile products.

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